871 CHAPTER 8 Test Find the indicated part of each triangle ABC. 1. Find C if A = 25.2°, a = 6.92 yd, and b = 4.82 yd. 2. Find c if C = 118°, a = 75.0 km, and b = 131 km. 3. Find B if a = 17.3 ft, b = 22.6 ft, and c = 29.8 ft. Chapter 8 Test Solve each triangle ABC. 7. A = 60°, b = 30 m, c = 45 m 8. b = 1075 in., c = 785 in., C = 38° 30′ Work each problem. 9. Find the magnitude and the direction angle, to the nearest tenth, for the vector shown in the figure. x y –6 8 0 v u Solve each problem. 4. Find the area of triangle ABC if a = 14, b = 30, and c = 40. 5. Find the area of triangle XYZ shown here. 6. Given a = 10 and B = 150° in triangle ABC, determine the values of b for which A has (a) exactly one value (b) two possible values (c) no value. 12 Z Y X 6 308 10. For the vectors u = 8-1, 39 and v = 82, -69, find each of the following. (a) u + v (b) -3v (c) u # v (d) u 11. Find the measure of the angle u between u = 84, 39 and v = 81, 59 to the nearest tenth. Solve each problem. 12. Height of a Balloon The angles of elevation of a balloon from two points A and B on level ground are 24° 50′ and 47° 20′, respectively. As shown in the figure, points A, B, and C are in the same vertical plane and points A and B are 8.4 mi apart. Find the height of the balloon above the ground to the nearest tenth of a mile. 13. Horizontal and Vertical Components Find the horizontal and vertical components of the vector with magnitude 569 and direction angle 127.5° from the horizontal. Give your answer in the form 8a, b9 to the nearest unit. 14. Radio Direction Finders Radio direction finders are placed at points A and B, which are 3.46 mi apart on an east-west line, with A west of B. From A, the bearing of a certain illegal pirate radio transmitter is 48°, and from B the bearing is 302°. Find the distance between the transmitter and A to the nearest hundredth of a mile. C A B 47°209 8.4 mi 24°509
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