Pre-Calculus Name __________________________ Test Review (7.1 – 7.2) Date Due next class

SECTION 1 (Law of Sines I) Solve any triangle(s) that result from the given information. Draw and label figure/s first. 1. A = 66°, B = 34°, c = 12 2.

3. Because of prevailing winds, a tree grew so that it was leaning 6° from vertical. You are standing at a point 45 meters from the tree. The tree is leaning toward you and the angle of elevation from you to the top of the tree is 33°. Find the height of the tree.

4. An airplane flies from city A to city B, a distance of 100 miles, and then turns through an angle of 20° and heads toward city C, as shown in the figure below. If the distance from A to C is 300 miles, how far is city B from city C? (Use Law of Sines twice.)

SECTION 2 (Law of Sines II) Solve any triangle(s) that result from the given information. Draw and label figure/s first. 5. 6.

7. 8. An airplane is spotted by two observers who are 900 feet apart. As the airplane passes over the line joining them, each observer takes a sighting of the angle of elevation to the plane. The angles are 50° and 30°. How high is the airplane at that time?

β

α

a

b

SECTION 3 (Right Triangle TRIG) *Solve the triangle; round answers to the nearest hundredth. 9. c = 14, a = ______ b = ______ ______ 10. If b = 3 and α = 40º, find a, c, and β . 11. A sailor on a boat that is 100 meters from a cliff sights a lighthouse at the top of the cliff. The angle of elevation to the top of the lighthouse is 42° and the angle of elevation to the bottom of the lighthouse is 35°. Find the height of the lighthouse. 12. From a certain distance, the angle of elevation to the top of a building is 17°. At a point 50 meters closer to the building, the angle of elevation is 31°. Approximate the height of the building.

SECTION 4 (Miscellaneous)

13. Use Co-Function Identities from your notes to evaluate the following: _______ a) sin 25 _______ b) cot52

_______ a) _______ b)