Expert: Richard J. Raridon - 7/15/2010

Question
1.)Choose the correct function value for: cot 81.1°

2.)Choose the correct function value for: csc 23° 20'

3.)Choose the correct function value for: sin 26.57°

4.)Choose the correct function value for: sin 87° 53'

5.)Choose the correct function value for: cos 328.1°

6.)Choose the correct function value for: sin 312° 40'

7.)Choose the measure of the acute angle θ, where:
  cos θ = 0.8400

8.)Choose the measure of the acute angle θ, where:
  tan θ = 1.325

9.)Choose the measure of the acute angle θ, where:
   csc θ = 3.000

10.)Choose the measure of the acute angle θ, where:
   sin θ = 0.2654

11.)Choose the measure of the acute angle θ, where:
   cos θ = 0.2715

12.)Choose the measure of the acute angle θ, where:
   tan θ = 2.550

13.)Find the measure of two angles between 0° and 360° with the function value:
           cos θ = 0.7851

14.)Find the measure of the angles between 0° and 360° with the function value:
              sin θ = -0.8300

15.)Find the measure of two angles between 0° and 360° with the function value:
              tan θ = 0.6182

16.)Find the measure of an angle between 0° and 360° that satisfies the condition:

sin θ = -0.5212, 90° < θ < 270°

17.)   Find the measure of an angle between 0° and 360° that satisfies the condition:

cos θ = 0.7815, tan θ < 0

18.)A boy is flying a kite and is standing 30 feet from a point directly under the kite. If the string to the kite is 50 feet long, find the angle of the elevation of the kite.

19.)How far from the base of a building is the bottom of a 30 foot ladder that makes an angle of 75° with the ground?

20.)The approach pattern to an airport requires pilots to set an 11° angle of descent toward a runway. If a plane is flying at an altitude of 9,500 m, at what distance (measured along the ground) from the airport must the pilot descend?

21.)   Opposite corners of a small rectangular park are joined by diagonal paths, each 360 m long. What are the dimensions of the park if the paths intersect at a 65° angle?

22.)A camping tent is supported by a rope stretched between two trees at a height of 210 cm. If the sides of the tent make an angle of 55° with the level ground, how wide is the tent at the bottom?

23.)From a point 250 m from the base of a vertical cliff, the angles of elevation to the top and bottom of a radio tower on top of the cliff are 62.2° and 59.5°. How tall is the tower?

24.)A plane is flying at an altitude of 24,300 m. From the plane, the measure of the angle of depression of a ship is 29°32'. How many meters, to three significant digits, does the plane have to fly before it is directly over the ship (assuming the ship is not moving)?

25.)The captain of a ship wants to determine his distance from shore. Seeking a familiar landmark, he finds a 90-ft-high lighthouse on top of a cliff. He sights both the top and bottom of the lighthouse. The measures of the two angles of elevation are 46 and 39. How far, to two significant digits, is he from the base of the cliff?

26.)The angle of elevation is 19°20' from a ship at sea to the top of a 159 ft lighthouse. Find, to three significant digits, the distance of the ship from the base of the lighthouse.

27.)At a point on the ground 27.6 m from the foot of a flagpole, the angle of elevation of the top of the pole is 29°50'. Find the height of the pole to three significant digits.

28.)From a point 450 ft from the base of a building, the angles of elevation of the top and bottom of a flagpole on top of the building have measures 60° and 55°. Find the height of the flagpole to two significant digits.

29.)Jane wants to find the height of a mountain. From some spot on the ground, she finds the angle of elevation to the top of the mountain to be 35° 20'. After moving 1,000 m closer to the mountain, she now finds the angle of elevation to be 50° 30'. Find the height of the mountain to three significant digits.

30.)Two tanks on a training mission are 1,800 m apart on a straight road. The drivers find the angles of elevation to the helicopter hovering over the road between them to be 33° and 52°. Find the height of the helicopter to two significant digits.

31.)The length of the longer leg of a right triangle is 2 more than twice the length of the shorter leg. The length of the hypotenuse is 1 more than the length of the longer leg. Find the measure, to the nearest degree, of the angle between the shorter leg and the hypotenuse.

Answer
I don't mind working a lot of problems but the first 17 you could have gotten using a calculator.  
1- 0.157
2- 2.525
3- 0.447
4- 0.9993
5- 0.849
6- -0.735
7- 32.86
8- 52.96
9- 19.47
10- 15.39
11- 74.25
12- 68.59
13- 38.27, 321.73
14- 236.1, 303.9
15- 31.72, 211.72
16- 211.41
17- -38.63
18- 53.13
19- 7.76 ft
20- 48873
21- 193x304
22- 294 cm
23- 56 m
24- 43200 m
25- 400 ft
26- 453 ft
27- 15.8 m
28- 137 ft
29- 1410 m
30- 760 m
31- 67.4