866 CHAPTER 8 Applications of Trigonometry Solve each problem. 25. Distance across a Canyon To measure the distance AB across a canyon for a power line, a surveyor measures angles B and C and the distance BC, as shown in the figure. What is the distance from A to B? 26. Length of a Brace A banner on an 8.0-ft pole is to be mounted on a building at an angle of 115°, as shown in the figure. Find the length of the brace. 27. Height of a Tree A tree leans at an angle of 8.0° from the vertical. From a point 7.0 m from the bottom of the tree, the angle of elevation to the top of the tree is 68°. Find the slanted height x in the figure. Canyon 58.4° 27.9° 125 ft A B C 8.0 ft 228 Brace 1158 688 8.08 7.0 m x 9. Given a = 10 and B = 30° in triangle ABC, for what values of b does A have (a) exactly one value (b) two possible values (c) no value? 10. Why can there be no triangle ABC satisfying A = 140°, a = 5, and b = 7? Solve each triangle ABC. 17. A = 25.2°, a = 6.92 yd, b = 4.82 yd 18. A = 61.7°, a = 78.9 m, b = 86.4 m 19. a = 27.6 cm, b = 19.8 cm, C = 42° 30′ 20. a = 94.6 yd, b = 123 yd, c = 109 yd Find the area of each triangle ABC. 21. b = 840.6 m, c = 715.9 m, A = 149.3° 22. a = 6.90 ft, b = 10.2 ft, C = 35° 10′ 23. a = 0.913 km, b = 0.816 km, c = 0.582 km 24. a = 43 m, b = 32 m, c = 51 m Use the law of cosines to find the indicated part of each triangle ABC. 11. Find A if a = 86.14 in., b = 253.2 in., c = 241.9 in. 12. Find b if B = 120.7°, a = 127 ft, c = 69.8 ft. 13. Find a if A = 51° 20′, c = 68.3 m, b = 58.2 m. 14. Find B if a = 14.8 m, b = 19.7 m, c = 31.8 m. 15. Find a if A = 60°, b = 5.0 cm, c = 21 cm. 16. Find A if a = 13 ft, b = 17 ft, c = 8 ft.
RkJQdWJsaXNoZXIy NjM5ODQ=