True or False: The lengths could NOT be lengths of the sides of a right triangle?

22, 32, and 16

True or False: The lengths could NOT be lengths of the sides of a right triangle?

5, 40, and 35

True or False: The lengths could NOT be lengths of the sides of a right triangle?

43, 1, and 43

True or False: The lengths could NOT be lengths of the sides of a right triangle?

17, 35, and 9

True or False: The lengths could NOT be lengths of the sides of a right triangle?

24, 10, and 15

True or False: The lengths could NOT be lengths of the sides of a right triangle?

42, 31, and 32

True or False: The lengths could NOT be lengths of the sides of a right triangle?

30, 2, and 29

True or False: The lengths could NOT be lengths of the sides of a right triangle?

8, 44, and 6

True or False: The lengths could NOT be lengths of the sides of a right triangle?

32, 17, and 20

True or False: The lengths could NOT be lengths of the sides of a right triangle?

6, 12, and 11

Can the lengths form a right triangle?

17, 18, and 8

Can the lengths form a right triangle?

21, 14, and 33

Can the lengths form a right triangle?

3, 26, and 27

Can the lengths form a right triangle?

2, 4, and 1

Can the lengths form a right triangle?

24, 13, and 21

Can the lengths form a right triangle?

13, 16, and 11

Can the lengths form a right triangle?

9, 15, and 2

Can the lengths form a right triangle?

9, 8, and 13

Can the lengths form a right triangle?

10, 1, and 10

Can the lengths form a right triangle?

3, 13, and 4

Which trigonometric function would you use to find the length of the hypotenuse of a right triangle if you only have the length of the other leg and one acute angle?

Which trigonometric function would you use to find the length of one leg of a right triangle if you only have the length of the hypotenuse and one adjacent angle?

Which trigonometric function would you use to find the length of one leg of a right triangle if you only have the length of the hypotenuse and one adjacent angle?

Which trigonometric function would you use to find the length of one leg of a right triangle if you only have the length of the other leg and one acute angle?

Which trigonometric function would you use to find the length of one leg of a right triangle if you only have the length of the other leg and one acute angle?

Which trigonometric function would you use to find the length of the hypotenuse of a right triangle if you only have the length of the other leg and one acute angle?

Which trigonometric function would you use to find the length of one leg of a right triangle if you only have the length of the other leg and one acute angle?

Which trigonometric function would you use to find the length of one leg of a right triangle if you only have the length of the other leg and one acute angle?

Which trigonometric function would you use to find the length of one leg of a right triangle if you only have the length of the hypotenuse and one adjacent angle?

Which trigonometric function would you use to find the length of one leg of a right triangle if you only have the length of the other leg and one acute angle?

What type of triangle is formed with sides of 14 m, 22 m, and 17 m in length?

What type of triangle is formed with sides of 7 m, 26 m, and 9 m in length?

What type of triangle is formed with sides of 11 m, 11 m, and 10 m in length?

What type of triangle is formed with sides of 20 m, 17 m, and 8 m in length?

What type of triangle is formed with sides of 20 m, 16 m, and 30 m in length?

What type of triangle is formed with sides of 29 m, 16 m, and 29 m in length?

What type of triangle is formed with sides of 23 m, 28 m, and 47 m in length?

What type of triangle is formed with sides of 22 m, 26 m, and 30 m in length?

What type of triangle is formed with sides of 27 m, 6 m, and 22 m in length?

What type of triangle is formed with sides of 16 m, 10 m, and 22 m in length?

A siloh casts a shadow of 48 feet. If the angle of elevation is 18 degrees, which is the closest to the distance from the top of the siloh to the tip of the shadow?

A siloh casts a shadow of 77 feet. If the angle of elevation is 61 degrees, which is the closest to the distance from the top of the siloh to the tip of the shadow?

A siloh casts a shadow of 47 feet. If the angle of elevation is 49 degrees, which is the closest to the distance from the top of the siloh to the tip of the shadow?

A flag pole casts a shadow of 95 feet. If the angle of elevation is 75 degrees, which is the closest to the distance from the top of the flag pole to the tip of the shadow?

A windmill casts a shadow of 117 feet. If the angle of elevation is 34 degrees, which is the closest to the distance from the top of the windmill to the tip of the shadow?

A siloh casts a shadow of 83 feet. If the angle of elevation is 18 degrees, which is the closest to the distance from the top of the siloh to the tip of the shadow?

A windmill casts a shadow of 79 feet. If the angle of elevation is 47 degrees, which is the closest to the distance from the top of the windmill to the tip of the shadow?

A flag pole casts a shadow of 32 feet. If the angle of elevation is 84 degrees, which is the closest to the distance from the top of the flag pole to the tip of the shadow?

A windmill casts a shadow of 43 feet. If the angle of elevation is 72 degrees, which is the closest to the distance from the top of the windmill to the tip of the shadow?

A totem pole casts a shadow of 102 feet. If the angle of elevation is 42 degrees, which is the closest to the distance from the top of the totem pole to the tip of the shadow?

A square is length 24 inches long. What is the length of the diagonal?

A square is length 16 inches long. What is the length of the diagonal?

A square is length 12 inches long. What is the length of the diagonal?

A square is length 22 inches long. What is the length of the diagonal?

A square is length 8 inches long. What is the length of the diagonal?

A square is length 25 inches long. What is the length of the diagonal?

A square is length 14 inches long. What is the length of the diagonal?

A square is length 22 inches long. What is the length of the diagonal?

A square is length 11 inches long. What is the length of the diagonal?

A square is length 9 inches long. What is the length of the diagonal?

An 25-foot ramp needs to be elevated at an angle measuring 6 degrees to the level with a step. Approximately how far does the ramp need to be away to hit the edge of the step?

An 24-foot ramp needs to be elevated at an angle measuring 6 degrees to the level with a step. Approximately how far does the ramp need to be away to hit the edge of the step?

An 21-foot ramp needs to be elevated at an angle measuring 6 degrees to the level with a step. Approximately how far does the ramp need to be away to hit the edge of the step?

An 25-foot ramp needs to be elevated at an angle measuring 16 degrees to the level with a step. Approximately how far does the ramp need to be away to hit the edge of the step?

An 15-foot ramp needs to be elevated at an angle measuring 19 degrees to the level with a step. Approximately how far does the ramp need to be away to hit the edge of the step?

An 10-foot ramp needs to be elevated at an angle measuring 14 degrees to the level with a step. Approximately how far does the ramp need to be away to hit the edge of the step?

An 19-foot ramp needs to be elevated at an angle measuring 4 degrees to the level with a step. Approximately how far does the ramp need to be away to hit the edge of the step?

An 22-foot ramp needs to be elevated at an angle measuring 4 degrees to the level with a step. Approximately how far does the ramp need to be away to hit the edge of the step?

An 21-foot ramp needs to be elevated at an angle measuring 1 degrees to the level with a step. Approximately how far does the ramp need to be away to hit the edge of the step?

An 14-foot ramp needs to be elevated at an angle measuring 14 degrees to the level with a step. Approximately how far does the ramp need to be away to hit the edge of the step?

A right triangle with one angle of 61 degrees has the adjacent leg measures 29 cm. What is the length of the hypotenuse to the nearest hundreth place?

A right triangle with one angle of 11 degrees has the adjacent leg measures 29 cm. What is the length of the hypotenuse to the nearest hundreth place?

A right triangle with one angle of 53 degrees has the adjacent leg measures 28 cm. What is the length of the hypotenuse to the nearest hundreth place?

A right triangle with one angle of 27 degrees has the adjacent leg measures 19 cm. What is the length of the hypotenuse to the nearest hundreth place?

A right triangle with one angle of 38 degrees has the adjacent leg measures 12 cm. What is the length of the hypotenuse to the nearest hundreth place?

A right triangle with one angle of 63 degrees has the adjacent leg measures 11 cm. What is the length of the hypotenuse to the nearest hundreth place?

A right triangle with one angle of 54 degrees has the adjacent leg measures 7 cm. What is the length of the hypotenuse to the nearest hundreth place?

A right triangle with one angle of 11 degrees has the adjacent leg measures 21 cm. What is the length of the hypotenuse to the nearest hundreth place?

A right triangle with one angle of 39 degrees has the adjacent leg measures 8 cm. What is the length of the hypotenuse to the nearest hundreth place?

A right triangle with one angle of 21 degrees has the adjacent leg measures 4 cm. What is the length of the hypotenuse to the nearest hundreth place?

Adam needs to build a shed and he can only use triangular frames that form a right triangle for the walls. Which of the following dimensions for a triangular frame should Adam use?

Adam needs to build a shed and he can only use triangular frames that form a right triangle for the walls. Which of the following dimensions for a triangular frame should Adam use?

Adam needs to build a shed and he can only use triangular frames that form a right triangle for the walls. Which of the following dimensions for a triangular frame should Adam use?

Adam needs to build a shed and he can only use triangular frames that form a right triangle for the walls. Which of the following dimensions for a triangular frame should Adam use?

Adam needs to build a shed and he can only use triangular frames that form a right triangle for the walls. Which of the following dimensions for a triangular frame should Adam use?

Adam needs to build a shed and he can only use triangular frames that form a right triangle for the walls. Which of the following dimensions for a triangular frame should Adam use?

Adam needs to build a shed and he can only use triangular frames that form a right triangle for the walls. Which of the following dimensions for a triangular frame should Adam use?

Adam needs to build a shed and he can only use triangular frames that form a right triangle for the walls. Which of the following dimensions for a triangular frame should Adam use?

Adam needs to build a shed and he can only use triangular frames that form a right triangle for the walls. Which of the following dimensions for a triangular frame should Adam use?

Adam needs to build a shed and he can only use triangular frames that form a right triangle for the walls. Which of the following dimensions for a triangular frame should Adam use?

Ashley needs to build a bridge to go across a pond. He has been able to collect the measurements forming a right triangle with one angle of 79 degrees and the adjacent side is 25 feet. If the bridge needs to be as long as the other leg, then about how long does the bridge need to be?

Micah needs to build a bridge to go across a pond. He has been able to collect the measurements forming a right triangle with one angle of 73 degrees and the adjacent side is 109 feet. If the bridge needs to be as long as the other leg, then about how long does the bridge need to be?

Eve needs to build a bridge to go across a pond. He has been able to collect the measurements forming a right triangle with one angle of 31 degrees and the adjacent side is 79 feet. If the bridge needs to be as long as the other leg, then about how long does the bridge need to be?

Adam needs to build a bridge to go across a pond. He has been able to collect the measurements forming a right triangle with one angle of 29 degrees and the adjacent side is 84 feet. If the bridge needs to be as long as the other leg, then about how long does the bridge need to be?

Keith needs to build a bridge to go across a pond. He has been able to collect the measurements forming a right triangle with one angle of 83 degrees and the adjacent side is 95 feet. If the bridge needs to be as long as the other leg, then about how long does the bridge need to be?

Elise needs to build a bridge to go across a pond. He has been able to collect the measurements forming a right triangle with one angle of 41 degrees and the adjacent side is 63 feet. If the bridge needs to be as long as the other leg, then about how long does the bridge need to be?

Sally needs to build a bridge to go across a pond. He has been able to collect the measurements forming a right triangle with one angle of 69 degrees and the adjacent side is 66 feet. If the bridge needs to be as long as the other leg, then about how long does the bridge need to be?

Micah needs to build a bridge to go across a pond. He has been able to collect the measurements forming a right triangle with one angle of 60 degrees and the adjacent side is 71 feet. If the bridge needs to be as long as the other leg, then about how long does the bridge need to be?

Elise needs to build a bridge to go across a pond. He has been able to collect the measurements forming a right triangle with one angle of 38 degrees and the adjacent side is 22 feet. If the bridge needs to be as long as the other leg, then about how long does the bridge need to be?

Elise needs to build a bridge to go across a pond. He has been able to collect the measurements forming a right triangle with one angle of 11 degrees and the adjacent side is 76 feet. If the bridge needs to be as long as the other leg, then about how long does the bridge need to be?

A shelf is supported with right triangle brackets that form 45 degrees where it meets the wall 25 inches below the shelf. What is the depth of the shelf?

A shelf is supported with right triangle brackets that form 45 degrees where it meets the wall 29 inches below the shelf. What is the depth of the shelf?

A shelf is supported with right triangle brackets that form 45 degrees where it meets the wall 30 inches below the shelf. What is the depth of the shelf?

A shelf is supported with right triangle brackets that form 45 degrees where it meets the wall 27 inches below the shelf. What is the depth of the shelf?

A shelf is supported with right triangle brackets that form 45 degrees where it meets the wall 28 inches below the shelf. What is the depth of the shelf?

A shelf is supported with right triangle brackets that form 45 degrees where it meets the wall 29 inches below the shelf. What is the depth of the shelf?

A shelf is supported with right triangle brackets that form 45 degrees where it meets the wall 22 inches below the shelf. What is the depth of the shelf?

A shelf is supported with right triangle brackets that form 45 degrees where it meets the wall 15 inches below the shelf. What is the depth of the shelf?

A shelf is supported with right triangle brackets that form 45 degrees where it meets the wall 30 inches below the shelf. What is the depth of the shelf?

A shelf is supported with right triangle brackets that form 45 degrees where it meets the wall 28 inches below the shelf. What is the depth of the shelf?

An 112 inch long diagonal in a rectangle makes an angle of 84 degrees with a length of the rectangle. What is the length of the rectangle to the nearest tenth?

An 112 inch long diagonal in a rectangle makes an angle of 30 degrees with a length of the rectangle. What is the length of the rectangle to the nearest tenth?

An 119 inch long diagonal in a rectangle makes an angle of 25 degrees with a length of the rectangle. What is the length of the rectangle to the nearest tenth?

An 100 inch long diagonal in a rectangle makes an angle of 54 degrees with a length of the rectangle. What is the length of the rectangle to the nearest tenth?

An 68 inch long diagonal in a rectangle makes an angle of 67 degrees with a length of the rectangle. What is the length of the rectangle to the nearest tenth?

An 60 inch long diagonal in a rectangle makes an angle of 17 degrees with a length of the rectangle. What is the length of the rectangle to the nearest tenth?

An 106 inch long diagonal in a rectangle makes an angle of 52 degrees with a length of the rectangle. What is the length of the rectangle to the nearest tenth?

An 105 inch long diagonal in a rectangle makes an angle of 72 degrees with a length of the rectangle. What is the length of the rectangle to the nearest tenth?

An 66 inch long diagonal in a rectangle makes an angle of 50 degrees with a length of the rectangle. What is the length of the rectangle to the nearest tenth?

An 35 inch long diagonal in a rectangle makes an angle of 37 degrees with a length of the rectangle. What is the length of the rectangle to the nearest tenth?

A siloh casts a 94 m shadow when the angle of elevation to the sun is 42 degrees. Approximately how tall is the siloh?

A windmill casts a 53 m shadow when the angle of elevation to the sun is 53 degrees. Approximately how tall is the windmill?

A windmill casts a 53 m shadow when the angle of elevation to the sun is 29 degrees. Approximately how tall is the windmill?

A totem pole casts a 112 m shadow when the angle of elevation to the sun is 27 degrees. Approximately how tall is the totem pole?

A tree casts a 88 m shadow when the angle of elevation to the sun is 21 degrees. Approximately how tall is the tree?

A tree casts a 87 m shadow when the angle of elevation to the sun is 13 degrees. Approximately how tall is the tree?

A flag pole casts a 33 m shadow when the angle of elevation to the sun is 36 degrees. Approximately how tall is the flag pole?

A totem pole casts a 26 m shadow when the angle of elevation to the sun is 20 degrees. Approximately how tall is the totem pole?

A siloh casts a 118 m shadow when the angle of elevation to the sun is 32 degrees. Approximately how tall is the siloh?

A totem pole casts a 116 m shadow when the angle of elevation to the sun is 73 degrees. Approximately how tall is the totem pole?

What is the length of an altitude of an equilateral triangle with a perimeter of 113 inches?

What is the length of an altitude of an equilateral triangle with a perimeter of 27 inches?

What is the length of an altitude of an equilateral triangle with a perimeter of 112 inches?

What is the length of an altitude of an equilateral triangle with a perimeter of 35 inches?

What is the length of an altitude of an equilateral triangle with a perimeter of 107 inches?

What is the length of an altitude of an equilateral triangle with a perimeter of 82 inches?

What is the length of an altitude of an equilateral triangle with a perimeter of 106 inches?

What is the length of an altitude of an equilateral triangle with a perimeter of 35 inches?

What is the length of an altitude of an equilateral triangle with a perimeter of 101 inches?

What is the length of an altitude of an equilateral triangle with a perimeter of 92 inches?

What is the length of an altitude of an equilateral triangle with a side length of 3 inches?

What is the length of an altitude of an equilateral triangle with a side length of 11 inches?

What is the length of an altitude of an equilateral triangle with a side length of 13 inches?

What is the length of an altitude of an equilateral triangle with a side length of 17 inches?

What is the length of an altitude of an equilateral triangle with a side length of 14 inches?

What is the length of an altitude of an equilateral triangle with a side length of 9 inches?

What is the length of an altitude of an equilateral triangle with a side length of 11 inches?

What is the length of an altitude of an equilateral triangle with a side length of 17 inches?

What is the length of an altitude of an equilateral triangle with a side length of 26 inches?

What is the length of an altitude of an equilateral triangle with a side length of 20 inches?

What is the length of a diagonal of a square with a perimeter of 89 inches?

What is the length of a diagonal of a square with a perimeter of 72 inches?

What is the length of a diagonal of a square with a perimeter of 62 inches?

What is the length of a diagonal of a square with a perimeter of 75 inches?

What is the length of a diagonal of a square with a perimeter of 77 inches?

What is the length of a diagonal of a square with a perimeter of 55 inches?

What is the length of a diagonal of a square with a perimeter of 97 inches?

What is the length of a diagonal of a square with a perimeter of 119 inches?

What is the length of a diagonal of a square with a perimeter of 46 inches?

What is the length of a diagonal of a square with a perimeter of 87 inches?

What is the perimeter of a square if the length of one of the diagonals is 30 cm?

What is the perimeter of a square if the length of one of the diagonals is 2 cm?

What is the perimeter of a square if the length of one of the diagonals is 17 cm?

What is the perimeter of a square if the length of one of the diagonals is 22 cm?

What is the perimeter of a square if the length of one of the diagonals is 27 cm?

What is the perimeter of a square if the length of one of the diagonals is 4 cm?

What is the perimeter of a square if the length of one of the diagonals is 4 cm?

What is the perimeter of a square if the length of one of the diagonals is 5 cm?

What is the perimeter of a square if the length of one of the diagonals is 29 cm?

What is the perimeter of a square if the length of one of the diagonals is 28 cm?

A right triangle with one angle of 18 degrees has the a hypotenuse of 69. What is the length of the leg adjacent to the 18 degree angle?

A right triangle with one angle of 11 degrees has the a hypotenuse of 69. What is the length of the leg adjacent to the 11 degree angle?

A right triangle with one angle of 75 degrees has the a hypotenuse of 21. What is the length of the leg adjacent to the 75 degree angle?

A right triangle with one angle of 66 degrees has the a hypotenuse of 51. What is the length of the leg adjacent to the 66 degree angle?

A right triangle with one angle of 52 degrees has the a hypotenuse of 103. What is the length of the leg adjacent to the 52 degree angle?

A right triangle with one angle of 13 degrees has the a hypotenuse of 42. What is the length of the leg adjacent to the 13 degree angle?

A right triangle with one angle of 49 degrees has the a hypotenuse of 41. What is the length of the leg adjacent to the 49 degree angle?

A right triangle with one angle of 13 degrees has the a hypotenuse of 80. What is the length of the leg adjacent to the 13 degree angle?

A right triangle with one angle of 72 degrees has the a hypotenuse of 71. What is the length of the leg adjacent to the 72 degree angle?

A right triangle with one angle of 39 degrees has the a hypotenuse of 97. What is the length of the leg adjacent to the 39 degree angle?

A right triangle with one angle of 74 degrees has the a hypotenuse of 77. What is the length of the leg farthest from the 74 degree angle?

A right triangle with one angle of 68 degrees has the a hypotenuse of 72. What is the length of the leg farthest from the 68 degree angle?

A right triangle with one angle of 50 degrees has the a hypotenuse of 60. What is the length of the leg farthest from the 50 degree angle?

A right triangle with one angle of 16 degrees has the a hypotenuse of 69. What is the length of the leg farthest from the 16 degree angle?

A right triangle with one angle of 62 degrees has the a hypotenuse of 35. What is the length of the leg farthest from the 62 degree angle?

A right triangle with one angle of 51 degrees has the a hypotenuse of 25. What is the length of the leg farthest from the 51 degree angle?

A right triangle with one angle of 41 degrees has the a hypotenuse of 32. What is the length of the leg farthest from the 41 degree angle?

A right triangle with one angle of 48 degrees has the a hypotenuse of 87. What is the length of the leg farthest from the 48 degree angle?

A right triangle with one angle of 61 degrees has the a hypotenuse of 91. What is the length of the leg farthest from the 61 degree angle?

A right triangle with one angle of 15 degrees has the a hypotenuse of 67. What is the length of the leg farthest from the 15 degree angle?

A 40 foot ladder leans against a wall. The foot of the ladder makes an angle of 81 degrees with the ground. How high up the wall does the top of the ladder reach?

A 80 foot ladder leans against a wall. The foot of the ladder makes an angle of 26 degrees with the ground. How high up the wall does the top of the ladder reach?

A 58 foot ladder leans against a wall. The foot of the ladder makes an angle of 80 degrees with the ground. How high up the wall does the top of the ladder reach?

A 39 foot ladder leans against a wall. The foot of the ladder makes an angle of 51 degrees with the ground. How high up the wall does the top of the ladder reach?

A 29 foot ladder leans against a wall. The foot of the ladder makes an angle of 33 degrees with the ground. How high up the wall does the top of the ladder reach?

A 43 foot ladder leans against a wall. The foot of the ladder makes an angle of 26 degrees with the ground. How high up the wall does the top of the ladder reach?

A 107 foot ladder leans against a wall. The foot of the ladder makes an angle of 35 degrees with the ground. How high up the wall does the top of the ladder reach?

A 22 foot ladder leans against a wall. The foot of the ladder makes an angle of 40 degrees with the ground. How high up the wall does the top of the ladder reach?

A 86 foot ladder leans against a wall. The foot of the ladder makes an angle of 11 degrees with the ground. How high up the wall does the top of the ladder reach?

A 108 foot ladder leans against a wall. The foot of the ladder makes an angle of 68 degrees with the ground. How high up the wall does the top of the ladder reach?

A ladder is leaning against a vertical house wall at an angle of 40 degrees. What is the measure of the angle between the ladder and the ground?

A ladder is leaning against a vertical house wall at an angle of 78 degrees. What is the measure of the angle between the ladder and the ground?

A ladder is leaning against a vertical house wall at an angle of 34 degrees. What is the measure of the angle between the ladder and the ground?

A ladder is leaning against a vertical house wall at an angle of 78 degrees. What is the measure of the angle between the ladder and the ground?

A ladder is leaning against a vertical house wall at an angle of 34 degrees. What is the measure of the angle between the ladder and the ground?

A ladder is leaning against a vertical house wall at an angle of 53 degrees. What is the measure of the angle between the ladder and the ground?

A ladder is leaning against a vertical house wall at an angle of 18 degrees. What is the measure of the angle between the ladder and the ground?

A ladder is leaning against a vertical house wall at an angle of 56 degrees. What is the measure of the angle between the ladder and the ground?

A ladder is leaning against a vertical house wall at an angle of 29 degrees. What is the measure of the angle between the ladder and the ground?

A ladder is leaning against a vertical house wall at an angle of 15 degrees. What is the measure of the angle between the ladder and the ground?

A boat is 103 meters from the base of a lighthouse out to sea. The lighthouse measures the angle of depression down to the boat to be 24 degrees. How far above sea level is the light on the lighthouse?

A boat is 104 meters from the base of a lighthouse out to sea. The lighthouse measures the angle of depression down to the boat to be 23 degrees. How far above sea level is the light on the lighthouse?

A boat is 57 meters from the base of a lighthouse out to sea. The lighthouse measures the angle of depression down to the boat to be 77 degrees. How far above sea level is the light on the lighthouse?

A boat is 35 meters from the base of a lighthouse out to sea. The lighthouse measures the angle of depression down to the boat to be 13 degrees. How far above sea level is the light on the lighthouse?

A boat is 35 meters from the base of a lighthouse out to sea. The lighthouse measures the angle of depression down to the boat to be 29 degrees. How far above sea level is the light on the lighthouse?

A boat is 77 meters from the base of a lighthouse out to sea. The lighthouse measures the angle of depression down to the boat to be 68 degrees. How far above sea level is the light on the lighthouse?

A boat is 63 meters from the base of a lighthouse out to sea. The lighthouse measures the angle of depression down to the boat to be 26 degrees. How far above sea level is the light on the lighthouse?

A boat is 86 meters from the base of a lighthouse out to sea. The lighthouse measures the angle of depression down to the boat to be 75 degrees. How far above sea level is the light on the lighthouse?

A boat is 48 meters from the base of a lighthouse out to sea. The lighthouse measures the angle of depression down to the boat to be 62 degrees. How far above sea level is the light on the lighthouse?

A boat is 116 meters from the base of a lighthouse out to sea. The lighthouse measures the angle of depression down to the boat to be 46 degrees. How far above sea level is the light on the lighthouse?

Adam took a short-cut across a rectangular yard 76 feet wide and 43 feet long. How much distance is saved by Adam cutting diagonally across the rectanglular yard?

Matthew took a short-cut across a rectangular yard 76 feet wide and 36 feet long. How much distance is saved by Matthew cutting diagonally across the rectanglular yard?

Andrew took a short-cut across a rectangular yard 99 feet wide and 95 feet long. How much distance is saved by Andrew cutting diagonally across the rectanglular yard?

Kayla took a short-cut across a rectangular yard 29 feet wide and 52 feet long. How much distance is saved by Kayla cutting diagonally across the rectanglular yard?

Kayla took a short-cut across a rectangular yard 67 feet wide and 31 feet long. How much distance is saved by Kayla cutting diagonally across the rectanglular yard?

Adam took a short-cut across a rectangular yard 29 feet wide and 100 feet long. How much distance is saved by Adam cutting diagonally across the rectanglular yard?

Adam took a short-cut across a rectangular yard 48 feet wide and 111 feet long. How much distance is saved by Adam cutting diagonally across the rectanglular yard?

Sally took a short-cut across a rectangular yard 86 feet wide and 44 feet long. How much distance is saved by Sally cutting diagonally across the rectanglular yard?

Kayla took a short-cut across a rectangular yard 26 feet wide and 57 feet long. How much distance is saved by Kayla cutting diagonally across the rectanglular yard?

Matthew took a short-cut across a rectangular yard 69 feet wide and 84 feet long. How much distance is saved by Matthew cutting diagonally across the rectanglular yard?

## Test generator

// Example program

#include <iostream>

#include <string>

#include <cmath>

#include <ctime>using namespace std;

void Skill1()

{

// This function adds a word problem asking the user to find the hypotenuse given two sides.

int a = rand()%100;

int b = rand()%100;

double c;

cout << “Billy is putting a fence daigonally through his garden. His garden is a rectangle “<< a <<” feet wide and ” << b << ” feet long. How long will his diagonal fence be? n n”;

}void Skill2()

{

cout << “Skill 2 n”;

}void Skill3()

{

cout << “Skill 3 n”;

}void Skill4()

{

cout << “Skill 4 n”;

}int main()

{

srand(time(0));

int userchoice;

do{

cout << “What type of question would you like to add? n”;

cin >> userchoice;

switch(userchoice)

{

case 1: Skill1();

break;

case 2: Skill2();

break;

case 3: Skill3();

break;

case 4: Skill4();

break;

default: cout <<“Goodbye”;

}

}while(userchoice!=0);

## ALL Chapter 4 Bookwork Rewritten with Answers

### Bookwork 4.2 #1-9

- Indicate which of the following are valid function declarations. Explain what is wrong with those that are invalid.
- round_tenth (double x);

*Answer: invalid, missing type return.* - double make_changes (X, Y);

*Answer: invalid missing types on formal parameters.* - int max (int x, int y, int z);

*Answer: valid.* - char sign (double x);

*Answer: valid.* - void output_string(apstring s);

*Answer: valid.*

- round_tenth (double x);
- Find all the error in each of the following functions:
- Code Snippet:

int average (int n1, int n2);

{

return N1 + N2 / 2;

}*Answer: The parameters are declared using lower case ‘n’, but the identifiers in the function block use uppercase ‘N’.*

- Code Snippet:

int total (int n1, int n2);

{

int sum;

return 0;

sum = n1+n2;

}*Answer: The return statement should be positioned so that it is after all computations have been completed.*

- Code Snippet:
- Write a function for each of the following:
- Round a real number to the nearest tenth.

*Answer: Code Snippet:*

*double round_tenths (double num)*

*{*

*double temp;**temp = num * 10; //multiplies original number by 10 therefore moving the decimal 1 place.*

*temp = temp +0.5; //adjust for rounding*

*temp = floor(temp); //truncates the value at the decimal point*

*return (temp/10); //moves decimal back 1 place.*

*}* - Round a real number to the nearest hundredth.

*Answer: Code Snippet:*

*double round_hundredths (double num)*

*{*

*double temp;**temp = num * 100; //multiplies original number by 100 therefore moving the decimal 2 places.*

*temp = temp +0.5; //adjust for rounding since we are using floor.*

*temp = floor(temp); //truncates the value at the decimal point (floor always rounds down).*

*return (temp/100); //moves decimal back 2 place.*

*}* - Convert degrees Fahrenheit to degrees Celsius.

*Answer: Code Snippet:*

*double change_scale (double fahrenheit)*

*{*

*return (5/9 * fahrenheit – 32); //subtracts 32 then multiplies by 5/9*

*}* - Compute the charge for cars at a parking lot; the rate is 75 cents per hour or any fraction thereof.

*Answer: Code Snippet:*

*double parking_charge (double hours)*

*{*

*int charged_hours;*const double RATE = 0.75;

*charged_hours = ceil(hours); //ceil always rounds up*

*return (charged_hours * RATE); //rate * time = total*

*}*

- Round a real number to the nearest tenth.
- Write a program that uses the function you wrote for calculating parking lot charges to print a ticket for a customer who parks in the parking lot. Assume the input is in minutes.

// Example program

#include <iostream>

#include <string>

#include <cmath>

using namespace std;double parking_charge (double hours)

{

int charged_hours;

const double RATE = 0.75; charged_hours = ceil(hours); //ceil always rounds up

return (charged_hours * RATE); //rate * time = total

}

int main()

{

double minutes;

cout << “How many minutes have you been parked here? n”;

cin >> minutes;

double hours = minutes/60.0;

cout << parking_charge(hours);

} - Write two functions (square and cube) to write a program which prints the square and cube of any user given integer.

// Example program

#include <iostream>

#include <string>

#include <cmath>

using namespace std;double square(int integer)

{

return integer*integer;

}double cube(int integer)

{

return integer*integer*integer;

}int main()

{

int userinteger;

cout << “Give me a number and I will square it and cube it for you. n”;

cin >> userinteger;cout << “The square of ” << userinteger << ” is “<< square(userinteger)<< “. and the cube of ” << userinteger << ” is ” << cube(userinteger)<< “.”;

} - Write a program that contains a function that allows the user to enter a base (a) and an exponent (x) and then have the program print the value of a to the x power.

Answer: This is a trick question. pow() does this.

// Example program

#include <iostream>

#include <string>

#include <cmath>

using namespace std;double power(double base, double exponent)

{

return pow(base, exponent);

}int main()

{

int userbase;

int userexponent;

cout << “Give me a base: n”;

cin >> userbase;

cout << “Give me an exponent: n”;

cin >> userexponent;

cout << userbase << ” to the “<< userexponent << ” is ” << power(userbase,userexponent) << “.”;

} - What role do parameters play in a function?

Answer: Parameters send values to functions via call statements.

- Explain the difference between formal parameters and actual parameters.

Answer: Formal parameters are listed in the parentheses of the function header. They must include the data type as well as the identifier name.

Actual parameters are listed in the parentheses of the call to the function. Only identifier names are listed. - Why is it a good idea to write functions that are as general as possible?

Answer: So they are reusable as many times as possible

### Bookwork 4.3 #1-3

- What is the difference between reference and value parameters?

*Answer: Value parameter is not to be changed and returned by the function, where the reference parameter is to be changed and sent back to the caller as new values.* - Write and test a function int_divide that receives two integer values and two integer variables from the caller. When the function completes the execution, the values in these variables should be the quotient and the remainder produced by dividing the second value by the first value. Be sure to name your parameters descriptively so as to aid the reader of the function.

*Answer: Code Snippet:*

*void int_divide (int divisor, int dividend, int "ient, int &remainder)*

*{*

*quotient = dividend / divisor;*

remainder = dividend % divisor;

*}* - When would you use a constant reference parameter?

*Answer: Constant reference parameters are used when the original data should not be altered by the function but the size of the data is relatively large.*

### Bookwork 4.4 #1-3

*All three questions combined into one programming challenge.*

Write a full program that has the following components.

- Basic program structure including an int main() which calls each of the following functions.
- A function called get_data which
- Prompts the user for an input integer and reads it.
- Receives nothing.
- Returns input integer (assumes non-negative).

- A function called compute_result which:
- Computes the square root of its argument.
- Receives integer value that was input.
- Returns square root of the input integer.

- A function called print_result which:
- Displays both the input integer and its square root.
- Receives integer input value and float square root.
- Returns nothing.

Answer: Code Snippet:

// Example program

#include <iostream>

#include <string>

#include <cmath>

using namespace std;int get_data()

{

int userinteger;cout << “Give me a positive integer and I will square root it for you.” << “n”;

cin >> userinteger;

return userinteger;

}double compute_result(int integer)

{

return sqrt(integer);

}void print_result(int integer, float root)

{

cout << “The square root of ” << integer << ” is approximately ” << root << “.”;

}

int main()

{

int userinteger = get_data();float root = compute_result(userinteger);

print_result(userinteger, root);

}

### Bookwork 4.5 #1-12

- Explain the difference between local and global identifiers.

Answer: Local identifiers are valid only in the main block or sunblock where they are declared. Global identifiers are valid in the main program block and all sunblocks. These are declared before the main block.

- State the advantages of using local identifiers.

Answer: The advantages of using local identifiers are:

1. They help to avoid side effects by eliminating the possibility of accidentally changing values in global variables.

2. They facilitate debugging.

3. They enhance the portability of functions.

4. They facilitate top-down design. - Discuss some appropriate uses for global identifiers. List several constants that would be appropriate global definitions.

Answer: Some appropriate uses of global identifiers are:

1. function names

2. type names

3. constants - What is meant by the scope of an identifier?

Answer: The scope of an identifier refers to the area(s) of the program where it may be used.

- SKIP
- Review the following program:

Code Snippet:

int main()

{

int a, b;

double x;

char ch;

…

}

int sub1 (int a1)

{

int b1;

…

}

int sub2(int a1, int b1)

{

double x1;

char ch1;

…

}- List all global variables.

Answer: No Global Variables

- List all local variables.

Answer: a, b, x, ch, b1, x1, ch1

- Indicate the scope of each identifier.

Answer:

Main program block: a, b, x, ch

sub1 function block: a1, b1

sub2 function block: a1, b1, x1, ch1

- List all global variables.
- SKIP
- SKIP
- SKIP
- SKIP
- SKIP
- Discuss the advantages and disadvantages of using the same names for identifiers in a subprogram and the main program.

Answer: Using the same names for identifiers both in the main program and in the function sunblocks allows the programmer to code quickly without having to think up and keep track of various variable names. However, a decision to reuse names may very likely lead to unwanted and unexpected side effects when variables change value when they are not supposed to. Also, duplicate names may not have the same meaning or purpose in different contexts.

### Bookwork 4.6 #1-4

- Why is it a good idea to put commonly used functions in a program library?

Answer: It is a good idea to put commonly used functions into a program library to allow easy access to a previously created function which can be applied in a new program. Library functions can be included in any program as it is needed.

- Discuss the difference between a library header file and a library implementation file. What are the roles and responsibilities of each file?

Answer: The library header file serves as the communication link between the implementation of its library and its users. Comments documenting the function go with the declarations in the header file.

The implementation file includes the library header file before defining the functions. This order is important because the compiler checks to make sure the function declarations in the header file match the headings in the implementations file. - Discuss how C++ preprocesses code in library files before compilation. Be sure to address the role of the directives
**#include**,**#ifndef**,**#define**, and**#endif**in this process.

Answer: The functions are declared and this code is saved in a library header file. The name of this file should have a .h extension so that it may be included in other programs. The implementation file contains the code that calls the library functions, and it should be saved with a cpp extension.

The directives #ifndef, #define, and #endif are used to prevent the compiler from including a library file more than one time in an application at compile time.

The first directive, #ifndef, asks if a file identifier has been defined. If it has, the library file has already been preprocessed and the compiler skips to the #endif at the end of the file. If the file identifier has not been defined, the preprocessor will get to the #define directive after preprocessing the library file. This directive then makes visible a global file identifier, so that subsequent inclusions after this one will behave as described in the paragraph above.

The #endif is used to signal the end of the library function.

In order to include user-defined library functions, the #include statement will use quotes around the header file name instead of the symbols used for the built-in library functions. - Create a program library named
**mymath**. This library should define functions for computing the areas of computing the areas of rectangles, circles, and triangles.

### Bookwork 4.7 #1-6

- Design, implement, and test a function for drawing parallelograms. Like a triangle, a parallelogram can be specified with three points.

*Answer: Code Snippet:*

void parallelogram (int x1, int y1, int x2, int y2, int x3, int, y3)

{

move(x1, y1);

lineto(x2, y2);

lineto(x3, y3);

lineto(x3-x2+x1,y3-y2+y1);

lineto(x1, y1);

} - SKIP
- Design, implement, and test a function for drawing rectangles that uses relative coordinates. The function should expect parameters that specify the coordinates of one corner and the rectangles height and width.

*Answer: Code Snippet:*

void rectangle (int x, int y, int length, int width)

{

move(x, y);

linerel(0, height);

linerel(width, 0);

linerel(0, -height);

linerel(-width, 0);

} - Design, implement, and test the
**fill_circle**function as mentioned in Example 4.8.

*Answer: Code Snippet:*

void fill_circle (int x, int y, int radius, int fill_pattern, int fill_color, int border_color)

{

int color = getcolor(); setcolor(border_color);

circle(x, y, radius);

setfillstyle(fill_pattern, fill_color);

floodfill(0, radius/2, border_color);

setcolor(color);

} - Rewrite the
**face**function of Example 4.7 so that it draws the eyes as filled circles.

*Answer: Code Snippet:*

void face (int center_x, int center_y, int size)

{

int color = getcolor(); circle(center_x, center_y, size);

fill_circle(center_x-size/4, center_y-size/4, 2, HATCH_FILL, BLUE, WHITE);

fill_circle(center_x+size/4, center_y+size/4, 2, HATCH_FILL, BLUE, WHITE); lineto(x3-x2+x1,y3-y2+y1);setcolor(color);

} - State two reasons why the development of programmer defined graphics functions is beneficial.

*Answer: The development of programmer-defined graphics functions is a good thing because:*

*1. it will extend the toolbox of graphics functions that are built into the compiler.*

*2. redundant code will be reduced to a function that will be called multiple times.*

*3. the task of drawing complex shapes can be simplified by creating functions for its component shapes.*

### Bookwork Chapter 4 Review #1-27

- Explain the difference between a value parameter and a reference parameter. Give an example of how each is used.

*Answer:*

A value parameter is used to pass to a function a copy of the value of a variable in the sunblock where the call statement is located. The receiving function then uses the copy of the value to perform whatever operations are defined for that function. For example, values are passed to a function where they are output in a complete sentence.

*A reference parameter may be used to send back new values from the function to the sunblock where the call statement is located or to received a value from the call statement in the sunblock, alter it, and substitute the adjusted value in place of the original. For example, a radius value is to be input in a get_data function and that value is to be used in another function that calculates the area of the circle having that radius value.* - Explain the difference between an actual parameter and a formal parameter.

Answer: Actual parameters are listed in the calling statement and consist only of the identifier names. Formal parameters are in the function heading and consist of both a data type and a name for each identifier.

- A function is declared as

**void sample_func(int a, double &b, char c);**

Which parameters in this declaration are reference parameters and which are value parameters?Answer: The reference parameter is b. The value parameters are a and c.

- Valid or invalid function call?

**sample_func(int1, double1, ch1);**

Answer: valid

- Valid or invalid function call?

**sample_func;**

*Answer: invalid – missing parentheses and parameter names* - Valid or invalid function call?

**sample_func();**

*Answer: invalid – missing parameter names* - Valid or invalid function call?

**sample_func(int int1, double double1, char ch1);**

*Answer: invalid – should not contain data types.* - Valid or invalid function call?

**sample_func(int1, double1);**

*Answer: invalid – function heading is expecting 3 parameters* - Valid or invalid function call?

**sample_func(int, double, char);**

*Answer: invalid – lists types rather than identifiers.* - Valid or invalid function call?

**sample_func(10, double1, ‘A’);**

*Answer: valid* - Valid or invalid function call?

**sample_func(10.5, double1, 66);**

*Answer: valid* - Valid or invalid function call?

**sample_func(10, 10.5, ‘A’);**

*Answer: invalid – second parameter needs to be a variable because it is a reference parameter.* - SKIP
- SKIP
- SKIP
- SKIP
- SKIP
- SKIP
- SKIP
- SKIP
- SKIP
- SKIP
- SKIP
- SKIP
- SKIP
- SKIP
- Why are reference parameters used in a function designed to initialize variables?

*Answer: Functions designed to only initialize variables, either by input or assignment, need to have those values passed on to other functions so that they can be used in any calculations and output that the program was written to do.*

## Bookwork 4.2 #1-9 Rewritten and Updated.

- Indicate which of the following are valid function declarations. Explain what is wrong with those that are invalid.
- round_tenth (double x);
- double make_changes (X, Y);
- int max (int x, int y, int z);
- char sign (double x);
- void output_string(apstring s);

- Find all the error in each of the following functions:
- Code Snippet:

int average (int n1, int n2);

{

return N1 + N2 / 2;

} - Code Snippet:

int total (int n1, int n2);

{

int sum;

return 0;

sum = n1+n2;

}

- Code Snippet:
- Write a function for each of the following:
- Round a real number to the nearest tenth.
- Round a real number to the nearest hundredth.
- Convert degrees Fahrenheit to degrees Celsius.
- Compute the charge for cars at a parking lot; the rate is 75 cents per hour or any fraction thereof.

- Write a program that uses the function you wrote for calculating parking lot charges to print a ticket for a customer who parks in the parking lot. Assume the input is in minutes.
- Write two functions (square and cube) to write a program which prints the square and cube of any user given integer.
- Write a program that contains a function that allows the user to enter a base (a) and an exponent (x) and then have the program print the value of a to the x power.
- What role do parameters play in a function?
- Explain the difference between formal parameters and actual parameters.
- Why is it a good idea to write functions that are as general as possible?

## Protected: Right Triangles Teacher’s Treatment Manual 2015

## Vocabulary Boxes

We did an activity with a piece of paper, some colored pencils, and some folding.

See Mr. V or Mr. M for more details.