Exam
Name___________________________________

ESSAY.  Write your answer in the space provided or on a separate sheet of paper.
Solve triangle ABC.  If necessary, round the answer to the nearest tenth.
1) 

2) 

Solve the triangle ABC. Round each answer to the nearest tenth when necessary.
3) 

Solve the triangle.  Round side lengths and angle measures to the nearest tenth when necessary.
4) 

5) 

Solve the problem.
6) Two tracking stations are on the equator 159 miles apart. A weather balloon is located on a bearing of  from the western station and on a bearing of  from the eastern station. How far is the balloon from the western station? Round to the nearest mile.

7) A rocket tracking station has two telescopes A and B placed 2.6 miles apart. The telescopes lock onto a rocket and transmit their angles of elevation to a computer after a rocket launch. What is the distance to the rocket from telescope B at the moment when both tracking stations are directly east of the rocket telescope A reports an angle of elevation of 23° and telescope B reports an angle of elevation of 56°?

8) A plane takes off from an airport on the bearing S29°W. It continues for 20 minutes then changes to bearing  and flies for 2 hours 20 minutes on this course then lands at a second airport. If the plane' s speed is 420 mph, how far from the first airport is the second airport? Round your answer correct to the nearest mile.

Find the area of the SAS triangle ABC. If necessary, round the answer to two decimal places.
9) A = 23°, b = 9 ft,  ft

Solve the equation on the interval 0 ≤ θ < 2π.
10) cos2 θ - 1 = 0

11) 2 sin2 θ = sin θ

12) cos2 θ + 2 cos θ + 1 = 0

13) csc5 θ - 4 csc θ = 0

14) 2 sin2 θ - 3 sin θ - 2 = 0

15) tan θ + sec θ = 1

16) sin2 θ - cos2 θ = 0

Use a calculator to solve the equation on the interval 0 ≤ θ < 2π. Round the answer to two decimal places.
17) tan θ = 3.4

18) 2 csc θ = 5

19) 2 cot θ = - 7

Solve the equation on the interval 0 ≤ θ < 2π.
20)  θ = 5(cos θ + 1)

Use a calculator to solve the equation on the interval 0 ≤ θ < 2π. Round the answer to two decimal places.
21) cos θ = -0.78

Solve the equation on the interval 0 ≤ θ < 2π.
22) (csc θ - 2)(cot θ + 1) = 0

23) tan2 θ = -  sec θ

24) sec2 θ - 2 = tan2 θ

Use a calculator to solve the equation on the interval 0 ≤ x < 2π.  Round the answer to one decimal place if necessary.
25) x + 3 sin x = 1

26) cos x + sin x = 2x

1) C = 103°, a = 9.4 m, b = 16.7 m
2) B = 37.2°, b = 283 ft, c = 350 ft
3) B ≈ 28.8° , C ≈ 26.2°, c ≈ 27.5 m
4) a ≈ 3.5, B = 30°, C = 90°
5) A ≈ 33.6°, B ≈ 112.9°, C ≈ 33.5°
6) 395 mi
7) 1.87 mi
8) 1110 mi
9) 3.52 sq ft
10) {0, π}
11) 
12) {π} 
13) 
14) 
15) {0}
16) 
17) {1.28, 4.42}
18) {0.41, 2.73}
19) 2.86, 6.01
20) {π}
21) {2.47, 3.82}
22) 
23) 
24) No solution
25) 0.3
26) 0.7