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Question : Find A. Round to the nearest thousandth of a degree if necessary : 2159842

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve for the requested quantity.

1) Find A. Round to the nearest thousandth of a degree if necessary.

A) A = 54.462°

B) A = 44.415°

C) A = 35.538°

D) A = 45.585°

2) Find b. Round to the nearest hundredth if necessary.

A) B = 581.35 ft

B) B = 532.15 ft

C) B = 525.76 ft

D) B = 534.62 ft

3) Find b. Round to the nearest hundredth if necessary.

A) B = -52.66 ft

B) B = -6.26 ft

C) B = 100.76 ft

D) B = 99.19 ft

4) Find b. Round to the nearest hundredth if necessary.

A) B = 3394.9 m

B) B = 3424.99 m

C) B = 3440.29 m

D) B = 3446.56 m

5) Find c. Round to the nearest hundredth if necessary.

A) C = 1079.8 m

B) C = 1106.02 m

C) C = 1093.37 m

D) C = 1073.37 m

Solve the right triangle.

6) A = 3.1 cm, B = 1.5 cm, C = 90°

A) A = 25.8°, B = 64.2°, C= 3.4 cm

B) A = 59.7°, B = 30.3°, C= 3.4 cm

C) A = 28.9°, B = 61.1°, C= 4.6 cm

D) A = 64.2°, B = 25.8°, C= 3.4 cm

7) A = 1.8 m, B = 39.8°, C = 90°

A) A = 50.2°, B = 2.8 m, C = 3.3 m

B) A = 50.2°, B = 2.8 m, C = 2.3 m

C) A = 50.2°, B = 1.5 m, C = 2.3 m

D) A = 50.2°, B = 0.4 m, C = 1.8 m

8) A = 2.7 in., A = 64.3°, C = 90°

A) B = 0.2 in., B = 25.7°, C = 2.7 in.

B) B = 3.0 in., B = 25.7°, C = 3.0 in.

C) B = 1.3 in., B = 25.7°, C = 3.0 in.

D) B = 3.0 in., B = 25.7°, C = 4.0 in.

9) B = 32.9°, C = 2.0 mm, C = 90°

A) A = 1.7 mm, A = 57.1°, B = 0.9 mm

B) A = 1.1 mm, A = 57.1°, B = 1.7 mm

C) A = 1.7 mm, A = 57.1°, B = 1.1 mm

D) A = 0.9 mm, A = 57.1°, B = 1.8 mm

10) A = 16° 45', C = 293 ft, C = 90°

A) B = 73° 14', A = 87.64 ft, B = 281.77 ft

B) B = 73° 15', A = 84.44 ft, B = 280.57 ft

C) B = 73° 15', A = 83.87 ft, B = 279.68 ft

D) B = 74° 14', A = 84.44 ft, B = 276.57 ft

11) A = 77° 53', C = 237 m, C = 90°

A) B = 13° -3', A = 231.92 m, B = 49.75 m

B) B = 12° 7', A = 231.92 m, B = 56.75 m

C) B = 12° 53', A = 232.92 m, B = 42.75 m

D) B = 12° 7', A = 231.72 m, B = 49.75 m

12) A = 36° 00', B = 47.1 m, C = 90°

A) B = 36° 00', A = 64.8 m, C = 38.1 m

B) B = 36° 00', A = 38.1 m, C = 34.2 m

C) B = 54° 00', A = 34.2 m, C = 58.2 m

D) B = 54° 00', A = 64.8 m, C = 80.1 m

13) B = 34° 00', B = 59.9 in., C = 90°

A) A = 56° 00', A = 88.8 in., C = 107.1 in.

B) A = 56° 00', A = 88.8 in., C = 72.3 in.

C) A = 34° 00', A = 40.4 in., C = 49.7 in.

D) A = 34° 00', A = 40.4 in., C = 107.1 in.

Solve the problem.

14) From a boat on the lake, the angle of elevation to the top of a cliff is 21°16’. If the base of the cliff is 413 feet from the boat, how high is the cliff (to the nearest foot)?

A) 164 ft

B) 171 ft

C) 161 ft

D) 174 ft

15) From a boat on the river below a dam, the angle of elevation to the top of the dam is 20°46’. If the dam is 1777 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?

A) 4686 ft

B) 4666 ft

C) 4676 ft

D) 4656 ft

16) From a balloon 886 feet high, the angle of depression to the ranger headquarters is 69°50’. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?

A) 325 ft

B) 315 ft

C) 330 ft

D) 320 ft

17) When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is 37°40’. If Joey is known to be standing 20 feet from the base of the tree, how tall is the tree (to the nearest foot)?

A) 21 ft

B) 19 ft

C) 15 ft

D) 17 ft

18) From the top of a vertical tower, 398 feet above the the surface of the earth, the angle of depression to a dog house is 22°1’. How far is it from the dog house to the foot of the tower? Round your answer to the hundredths place.

A) 984.26 ft

B) 996.66 ft

C) 1086.86 ft

D) 968.67 ft

19) A 37-foot ladder is leaning against the side of a building. If the ladder makes an angle of 22°27’. with the side of the building, how far is the bottom of the ladder from the base of the building? Round your answer to the hundredths place.

A) 19.83 ft

B) 4.76 ft

C) 15.43 ft

D) 14.13 ft

20) A 36-foot ladder is leaning against the side of a building. If the ladder makes an angle of 26°38’ with the side of the building, how far up from the ground does the ladder make contact with the building? Round your answer to the hundredths place.

A) 29.61 ft

B) 32.18 ft

C) 35.34 ft

D) 33.38 ft

21) A contractor needs to know the height of a building to estimate the cost of a job. From a point 94 feet away from the base of the building, the angle of elevation to the top of the building is found to be 50°52’. Find the height of the building. Round your answer to the hundredths place.

A) 118.43 ft

B) 119.76 ft

C) 114 ft

D) 115.53 ft

22) Find h as indicated in the figure. Round your answer to the hundredths place.

A) 131.17 ft

B) 128.35 ft

C) 122.6 ft

D) 126.05 ft

23) Find h as indicated in the figure. Round your answer to the hundredths place.

A) 59.63 m

B) 139.13 m

C) 39.13 m

D) 24.13 m

24) The angle of elevation from a point on the ground to the top of a tower is 35° 1’.

The angle of elevation from a point 146 feet farther back from the tower is 22° 17’. Find the height of the tower. Round your answer to the hundredths place.

A) 154.63 ft

B) 139.89 ft

C) 1441.25 ft

D) 144.13 ft

25) Bob is driving along a straight and level road straight toward a mountain. At some point on his trip he measures the angle of elevation to the top of the mountain and finds it to be 24°51’ He then drives 1 mile (1 mile = 5280 ft) more and measures the angle of elevation to be 35°25’. Find the height of the mountain to the nearest foot.

A) 70,122 ft

B) 7112 ft

C) 7012 ft

D) 701,216 ft

26) A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed the angle of depression to the boat is 14° 19’. When the boat stops, the angle of depression is 46° 25’. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.

A) 593.33ft

B) 615.83 ft

C) 638.53 ft

D) 578.03 ft

27) A person is watching a car from the top of a building. The car is traveling on a straight road directly toward the building. When first noticed the angle of depression to the car is 23° 30’. When the car stops, the angle of depression is 49° 1’. The building is 210 feet tall. How far did the car travel from when it was first noticed until it stopped? Round your answer to the hundredths place.

A) 300.52 ft

B) 500.62 ft

C) 326.73 ft

D) 279.45 ft

28) A person is watching a car from the top of a building. The car is traveling on a straight road away from the building. When first noticed the angle of depression to the car is 49° 8’. When the car stops, the angle of depression is 27° 32’. The building is 270 feet tall. How far did the car travel from when it was first noticed until it stopped? Round your answer to the hundredths place.

A) 310.53 ft

B) 484.42 ft

C) 284.32 ft

D) 263.25 ft

29) In one area, the lowest angle of elevation of the sun in winter is 27°36’ Find the minimum distance x that a plant needing full sun can be placed from a fence that is 5.9 feet high. Round your answer to the tenths place.

A) 14.7 ft

B) 10.9 ft

C) 11.3 ft

D) 11.5 ft

30) In one area, the lowest angle of elevation of the sun in winter is 20° 24’. A fence is to be built 12.6 ft away from a plant in the direction of the sun. (See drawing) Find the maximum height, x, for the fence so that the plant will get full sun. Round your answer to the tenths place.

A) 5 ft

B) 6.2 ft

C) 4 ft

D) 4.7 ft

31) A 4.1-ft fence is 11.143 ft away from a plant in the direction of the sun. It is observed that the shadow of the fence extends exactly to the bottom of the plant. (See drawing) Find θ, the angle of elevation of the sun at that time. Round the measure of the angle to the nearest tenth of a degree.

A) θ = 20.4°

B) θ = 21.6°

C) θ = 20.2°

D) θ = 20°

32) A fire is sighted due west of lookout A. The bearing of the fire from lookout B, 13.7 miles due south of A, is N 57°12'W. How far is the fire from B (to the nearest tenth of a mile)?

A) 27.3 mi

B) 28.3 mi

C) 26.3 mi

D) 25.3 mi

33) City X is 40 miles due south of City Y, and City Z is 85 miles due west of City X. What is the bearing of City Z from City Y (to the nearest tenth of a degree)?

A) S 66.8°W

B) S 65.8°W

C) S 64.8°W

D) S 63.8°W

34) A ship travels 58 km on a bearing of 20°, and then travels on a bearing of 110° for 146 km. Find the distance from the starting point to the end of the trip, to the nearest kilometer.

A) 55 km

B) 157 km

C) 20 km

D) 204 km

35) Radio direction finders are set up at points A and B, 2.51 mi apart on an east-west line. From A it is found that the bearing of a signal from a transmitter is N 51.1°E while from B it is N 38.9°W Find the distance of the transmitter from B, to the nearest hundredth of a mile.

A) 1.08 mi

B) 2.45 mi

C) 1.95 mi

D) 1.58 mi

36) To measure the width of a river, a surveyor starts at point A on one bank and walks 74 feet down the river to point B. He then measures the angle ABC to be 21°31’15” Estimate the width of the river to the nearest foot. See the figure below.

C

A 74 ft B

A) 69 ft

B) 188 ft

C) 27 ft

D) 29 ft

37) A racetracks curve is banked so that the outside of the curve is slightly elevated or inclined above the inside of the curve. This inclination is called the elevation of the track. The maximum speed on the track in miles per hour is given by

√r(29,000 + 41,000tanq)

where r is the radius of the track in miles and θ is the elevation in degrees. Find the maximum speed for a racetracks with an elevation of 26° and a radius of 0.6 miles Round to the nearest mile per hour.

A) 171 mph

B) 193 mph

C) 59,899 mph

D) 37,953 mph

38) When the angle of elevation of the sun is θ, a tree casts a shadow. Which trigonometric function models the length of the tree's shadow?

A) tanθ

B) cosθ

C) cotθ

D) sinθ

39) A formula used by an engineer to determine the radius of a curve, R, when designing a road is: R = V^{2}/30(0.1 + tanα where α is an angle of the road and V is the velocity (in feet per second) for which the curve is designed. If V = 67 ft per sec and α = 1.6° find R. Round your answer to the nearest tenth of a foot.

A) R = 1173 ft

B) R = 1179.8 ft

C) R = 1169.6 ft

D) R = 1166.9 ft

40) A formula used by an engineer to determine the radius of a curve, R, when designing a particular road is: R = V^{2}/30(0.1 + tanα where α is an angle of the road and V is the velocity (in feet per second) for which the curve is designed. If α = 3.2°, and R = 1655.67 ft find V. Round to the nearest foot per second.

A) V = 84 ft per sec

B) V = 88 ft per sec

C) V = 91 ft per sec

D) V = 86 ft per sec