Name ______________________________________________________ Date ________________________
1. If a 24-foot ladder makes a 58° angle with the ground, how many feet up the wall will it reach?
Round your answer to the nearest tenth.
Find the variable to the nearest tenth.
2. 3. 4.
5. Use special right triangles to solve for the variables.
6. Find the angle of elevation of the Sun when a 12.5-meter-tall telephone pole casts an 18-meter-long shadow.
7. The angle of elevation from a woman to the top of a hill is 49°. If the woman is 400 feet from the base of the hill, how high is the hill?
8. From the top of a 120-foot-high tower, an air traffic controller observes an airplane on the runway at an angle of depression of 19°. How far from the base of the tower is the airplane?
9. A ski run is 1000 yards long with a vertical drop of 208 yards. Find the angle of depression from the top of the ski run to the bottom
.

Use the Law of Sines or the Law of Cosines to answer problems #10-13.
Law of Sines: Law of Cosines:
=
=
2
2
2
10. In △ ABC, m∠A = 46, m∠B = 105, and c = 19.8. Find a to the nearest tenth.
A 29.4
F 7068.4
B 28.5 C 15.7 D 14.7
11. In △ LMN, ℓ = 42, m = 61, and m∠N = 108. Find n to the nearest tenth.
G 84.1 H 79.2 J 24.7
12. 13.
14. Rightsville is 120 miles due east of Johnstown and Macon is 80 miles directly south of Johnstown.
Find the shortest distance in kilometers between Macon and Rigthsville.
15. An eagle is traveling along a path due east at a rate of 50 miles per hour and the wind is blowing due north at 15 miles per hour. What is the magnitude of the resultant velocity of the eagle?
16. A jet begins a flight along a path due south at 250 miles per hour. A wind is blowing due west at
20 miles per hour. What is the plane’s resulting direction?
________degrees at _________ of __________
Find each of the following for
= ⟨-4, 6⟩,
= ⟨ 3, –8⟩ , and
= ⟨1, 5⟩.
17.
18 .
19.