Trigonometry Sample Exam #4 – Chapter 7 Complete all questions within 1 hour. Each question is equally weighted, please show all work. Solve the following triangles and state the case AAS, ASA, SAS, SSS, or SSA. 1. B = 13.4°, C = 24.8°, and a = 325 cm. 2. B = 56.3°, a = 8.3 cm, and b = 7.6 cm. 3. a = 42 cm, b = 12 cm, and c = 31 cm. Solve. 4. Find the area of a regular decagon (10-sided polygon) with sides measuring 6 centimeters. Round to the nearest tenth. 5. Two boats leave the harbor at the same time. The first boat is travelling at 15 miles per hour in the SW direction and the second boat is travelling due west at 12 miles per hour. How far apart are the boats after 2 hours? (Hint: Distance = Rate × Time) Given vectors u = 1, 2 , v =

= −4,3 , and w

5, −6 . Find the following:

6. 5u − v 7.

v+w

8. Find the angle between u and v.

9. A rifle cartridge is fired into the air with an initial velocity of 1,200 feet per second at an angle of 45°. Find the horizontal and vertical components of the velocity vector. 10. An airplane travelling due east at 255 miles per hour and the wind is blowing at a constant 25 miles per hour in the direction of N75°E. Find the true speed and bearing of the airplane.

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