Question 1

As shown in the diagram, the angle of elevation from a point on the ground to the top of the tree is 34°.  If the point is 20 feet from the base of the tree, what is the height of the tree, to the nearest tenth of a foot?

Accepted Answer

13.5

Answer

16.6

Answer

11.2

Answer

29.7

Question 2

The diagram shows a ramp connecting the ground to a loading platform 4.5 feet above the ground. The ramp measures 11.75 feet from the ground to the top of the loading platform.  Determine and state, to the nearest degree, the angle of elevation formed by the ramp and the ground.

Accepted Answer

23

Question 3

As shown in the diagram, a ship is heading directly toward a lighthouse whose beacon is 125 feet above sea level. At the first sighting, point A, the angle of elevation from the ship to the light was 7°. A short time later, at point D, the angle of elevation was 16°.  To the nearest foot, determine and state how far the ship traveled from point A to point D.

Accepted Answer

582

Question 4

A carpenter extends a ladder against a house to reach the bottom of a window 30 feet above the ground. The ladder makes a 70˚ angle with the ground. To the nearest foot, determine and state the length of the ladder.

Accepted Answer

Freetext://32

Question 5

A 20-foot support post leans against a wall, making a 70˚ angle with the ground. To the nearest tenth of a foot, how far up the wall will the support post reach?

Accepted Answer

18.8

Answer

6.9

Answer

18.7

Answer

6.8

Question 6

A ladder leans against a building. The top of the ladder touches the building 10 feet above the ground. The foot of the ladder is 4 feet from the building. Find, to the nearest degree, the angle that the ladder makes with the level ground.

Accepted Answer

68

Question 7

In the diagram, a window of a house is 15 feet above the ground. A ladder is placed against the house with its base at an angle of 75˚ with the ground. Determine and state the length of the ladder to the nearest tenth of a foot.

Accepted Answer

15.5

Question 8

As modeled, a movie is projected onto a large outdoor screen. The bottom of the 60-foot-tall screen is 12 feet off the ground. The projector sits on the ground at a horizontal distance of 75 feet from the screen.  Determine and state, to the nearest tenth of a degree, the measure of  $	heta$, the projection angle.

Accepted Answer

34.7˚

Question 9

A man was parasailing above a lake at an angle of elevation of 32° from a boat, as modeled in the diagram.  If 129.5 meters of cable connected the boat to the parasail, approximately how many meters above the lake was the man?

Accepted Answer

68.6

Answer

109.8

Answer

244.4

Answer

80.9

Question 10

Bob places an 18-foot ladder 6 feet from the base of his house and leans it up against the side of his house. Find, to the nearest degree, the measure of the angle the bottom of the ladder makes with the ground.

Accepted Answer

71˚

Question 11

As shown in the diagram, an island (I) is due north of a marina (M). A boat house (H) is 4.5 miles due west of the marina. From the boat house, the island is located at an angle of 54˚ from the marina.  Determine and state, to the nearest tenth of a mile, the distance from the boat house (H) to the island (I).

Accepted Answer

7.7

Question 12

As shown in the diagram, an island (I) is due north of a marina (M). A boat house (H) is 4.5 miles due west of the marina. From the boat house, the island is located at an angle of 54˚ from the marina.  Determine and state, to the nearest tenth of a mile, the distance from the island (I) to the marina (M).

Accepted Answer

6.2

Question 13

A ladder 20 feet long leans against a building, forming an angle of 71° with the level ground. To the nearest foot, how high up the wall of the building does the ladder touch the building?

Accepted Answer

19

Answer

15

Answer

18

Answer

16

Question 14

To build a handicapped-access ramp, the building code states that for every 1 inch of vertical rise in height, the ramp must extend out 12 inches horizontally, as shown in the diagram.  What is the angle of inclination, x, of this ramp, to the nearest hundredth of a degree?

Accepted Answer

4.76

Answer

4.78

Answer

85.22

Answer

85.24

Question 15

The map of a campground is shown. Campsite C, first aid station F, and supply station S lie along a straight path. The path from the supply station to the tower, T, is perpendicular to the path from the supply station to the campsite. The length of path FS is 400 feet. The angle formed by path TF and path FS is 72°. The angle formed by path     and path CS is 55°.  Determine and state, to the nearest foot, the distance from the campsite to the tower.

Accepted Answer

1503

Question 16

Yolanda is making a springboard to use for gymnastics. She has 8-inch-tall springs and wants to form a 16.5° angle with the base, as modeled in the diagram.  To the nearest tenth of an inch, what will be the length of the springboard, x?

Accepted Answer

28.2

Answer

8.3

Answer

27.0

Answer

2.3

Question 17

A homeowner is building three steps leading to a deck, as modeled by the diagram. All three step rises, HA, FG, and DE, are congruent, and all three step runs, HG, FE, and DC, are congruent. Each step rise is perpendicular to the step run it joins. The measure of ∠CAB = 36° and m∠CBA = 90°.  If each step run is parallel to AB and has a length of 10 inches, determine and state the length of each step rise, to the nearest tenth of an inch.

Accepted Answer

7.3

Question 18

A homeowner is building three steps leading to a deck, as modeled by the diagram. All three step rises, HA, FG, and DE, are congruent, and all three step runs, HG, FE, and DC, are congruent. Each step rise is perpendicular to the step run it joins. The measure of ∠CAB = 36° and m∠CBA = 90°.  If each step run is parallel to AB and has a length of 10 inches, determine and state the length of AC, to the nearest inch.

Accepted Answer

37

Question 19

From a point on the ground one-half mile from the base of a historic monument, the angle of elevation to its top is 11.87°. To the nearest FOOT, what is the height of the monument?

Accepted Answer

555

Answer

543

Answer

1086

Answer

1110

Question 20

As modeled in the diagram, an access ramp starts on flat ground and ends at the beginning of the top step. Each step is 6 inches tall and 8 inches deep.  If the angle of elevation of the ramp is 4.76˚, determine and state the length of the ramp, to the nearest tenth of a foot.

Accepted Answer

18.1

Question 21

As modeled in the diagram, an access ramp starts on flat ground and ends at the beginning of the top step. Each step is 6 inches tall and 8 inches deep.  If the angle of elevation of the ramp is 4.76˚, determine and state to the nearest tenth of a foot the horizontal distance, d, from the bottom of the stairs to the bottom of the ramp.

Accepted Answer

16.7

Question 22

A 12-foot ladder leans against a building and reaches a window 10 feet above ground. What is the measure of the angle, to the nearest degree, that the ladder forms with the ground?

Accepted Answer

56

Answer

40

Answer

50

Answer

34

Question 23

A support wire reaches from the top of a pole to a clamp on the ground. The pole is perpendicular to the level ground and the clamp is 10 feet from the base of the pole. The support wire makes a 68° angle with the ground. Find the length of the support wire to the nearest foot.

Accepted Answer

27

Question 24

Nick wanted to determine the length of one blade of the windmill. He stood at a point on the ground 440 feet from the windmill’s base. Using surveyor’s tools, Nick measured the angle between the ground and the highest point reached by the top blade and found it was 38.8°. He also measured the angle between the ground and the lowest point of the top blade, and found it was 30°.  Determine and state a blade’s length, x, to the nearest foot.

Accepted Answer

100

Question 25

Chelsea is sitting 8 feet from the foot of a tree. From where she is sitting, the angle of elevation of her line of sight to the top of the tree is 36°. If her line of sight starts 1.5 feet above ground, how tall is the tree, to the nearest foot?

Accepted Answer

7

Answer

6

Answer

8

Answer

5

Question 26

A 15-foot ladder leans against a wall and makes an angle of 65° with the ground. What is the horizontal distance from the wall to the base of the ladder, to the nearest tenth of a foot?

Accepted Answer

6.3

Answer

7.0

Answer

12.9

Answer

13.6

Question 27

An airplane took off at a constant angle of elevation. After the plane traveled for 25 miles, it reached an altitude of 5 miles.  To the nearest tenth of a degree, what was the angle of elevation?

Accepted Answer

11.5˚

Question 28

Diego needs to install a support beam to hold up his new birdhouse, as modeled below. The base of the birdhouse is 24$\frac{1}{2}$inches long. The support beam will form an angle of 38˚ with the vertical post. Determine and state the approximate length of the support beam, x, to the nearest inch.

Accepted Answer

40

Question 29

The center pole of a tent is 8 feet long, and a side of the tent is 12 feet long.  If a right angle is formed where the center pole meets the ground, what is the measure of angle A to the nearest degree?

Accepted Answer

42˚

Answer

48˚

Answer

34˚

Answer

56˚

Question 30

A tree casts a 25-foot shadow on a sunny day, as shown in the diagram.  If the angle of elevation from the tip of the shadow to the top of the tree is 32°, what is the height of the tree to the nearest tenth of a foot?

Accepted Answer

15.6

Answer

21.2

Answer

40.0

Answer

13.2

Question 31

A hot-air balloon is tied to the ground with two taut (straight) ropes, as shown in the diagram. One rope is directly under the balloon and makes a right angle with the ground. The other rope forms an angle of 50° with the ground.  Determine the height, to the nearest foot, of the balloon directly above the ground.

Accepted Answer

84

Question 32

A hot-air balloon is tied to the ground with two taut (straight) ropes, as shown in the diagram. One rope is directly under the balloon and makes a right angle with the ground. The other rope forms an angle of 50° with the ground.  Determine the distance, to the nearest foot, on the ground between the two ropes.

Accepted Answer

71

Question 33

As shown in the diagram, a ladder 5 feet long leans against a wall and makes an angle of 65° with the ground. Find, to the nearest tenth of a foot, the distance from the wall to the base of the ladder.

Accepted Answer

2.1

Question 34

A metal pipe is used to hold up a 9-foot fence, as shown in the diagram. The pipe makes an angle of 48° with the ground.  Determine, to the nearest foot, how far the bottom of the pipe is from the base of the fence.

Accepted Answer

8

Question 35

A metal pipe is used to hold up a 9-foot fence, as shown in the diagram. The pipe makes an angle of 48° with the ground.  Determine, to the nearest foot, the length of the metal pipe.

Accepted Answer

12

Question 36

A 28-foot ladder is leaning against a house.  The bottom of the ladder is 6 feet from the base of the house.  Find the measure of the angle formed by the ladder and the ground, to the nearest degree.

Accepted Answer

78

Question 37

A man standing on level ground is 1000 feet away from the base of a 350-foot-tall building.  Find, to the nearest degree, the measure of the angle of elevation to the top of the building from the point on the ground where the man is standing.

Accepted Answer

19

Question 38

Ron and Francine are building a ramp for performing skateboard stunts, as shown in the accompanying diagram.  The ramp is 7 feet long and 3 feet high.  What is the measure of the angle, x, that the ramp makes with the ground, to the nearest tenth of a degree?

Accepted Answer

25.4

Question 39

A person standing on level ground is 2,000 feet away from the foot of a 420-foot-tall building, as shown in the accompanying diagram.  To the nearest degree, what is the value of x?

Accepted Answer

12

Question 40

As shown in the diagram, a building casts a 72-foot shadow on the ground when the angle of elevation of the sun is 40°.  How tall is the building, to the nearest foot?

Accepted Answer

60

Answer

86

Answer

46

Answer

94

Question 41

As shown in the diagram, a ladder 12 feet long leans against a wall and makes an angle of 72° with the ground.  Find, to the nearest tenth of a foot, the distance from the wall to the base of the ladder.

Accepted Answer

3.7

Question 42

A stake is to be driven into the ground away from the base of a 50-foot pole, as shown in the diagram.  A wire from the stake on the ground to the top of the pole is to be installed at an angle of elevation of 52°.  How far away from the base of the pole should the stake be driven in, to the nearest foot?

Accepted Answer

39

Question 43

A stake is to be driven into the ground away from the base of a 50-foot pole, as shown in the diagram.  A wire from the stake on the ground to the top of the pole is to be installed at an angle of elevation of 52°.  What will be the length of the wire from the stake to the top of the pole, to the nearest foot?

Accepted Answer

63

Question 44

From the top of an apartment building, the angle of depression to a car parked on the street below is 38 degrees, as shown in the diagram.  The car is parked 80 feet from the base of the building.  Find the height of the building, to the nearest tenth of a foot.

Accepted Answer

62.5

Question 45

The top of a lighthouse, T, is 215 feet above sea level, L, as shown in the diagram.  The angle of depression from the top of the lighthouse to a boat, B, at sea is 26°.  Determine, to the nearest foot, the horizontal distance, x, from the boat to the base of the lighthouse.

Accepted Answer

441

Question 46

The tailgate of a truck is 2 feet above the ground.  The incline of a ramp used for loading the truck is 11°.  Find, to the nearest tenth of a foot, the length of the ramp.

Accepted Answer

10.5

Question 47

Joe is holding his kite string 3 feet above the ground, as shown in the diagram.  The distance between his hand and a point directly under the kite is 95 feet.  If the angle of elevation to the kite is 50°, find the height, h, of his kite, to the nearest foot.

Accepted Answer

116

Question 48

A surveyor needs to determine the distance across the pond shown in the accompanying diagram.  She determines that the distance from her position to point P on the south shore of the pond is 175 meters and the angle from her position to point X on the north shore is 32°.  Determine the distance, PX, across the pond, rounded to the nearest meter.

Accepted Answer

109

Question 49

A lighthouse is built on the edge of a cliff near the ocean, as shown in the accompanying diagram.  From a boat located 200 feet from the base of the cliff, the angle of elevation to the top of the cliff is 18° and the angle of elevation to the top of the lighthouse is 28°.  What is the height of the lighthouse, x, to the nearest tenth of a foot?

Accepted Answer

41.4

Question 50

A tree casts a shadow that is 20 feet long.  The angle of elevation from the end of the shadow to the top of the tree is 66°.  Determine the height of the tree, to the nearest foot.

Accepted Answer

45

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