CHAPTER 10 FURTHER APPLIC 63. The roof of a house is at a 20° angle. An 8-foot solar panel is to be mounted on the roof and should be angled 38° relative to the horizontal for optimal results. (See Figure 31). How long does the vertical support holding up the back of the panel need to be? Round to the nearest tenth. 8 ft 38° 20° Figure 31 65. A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 4.3 km apart, to be 32° and 56°, as shown in Figure 33. Find the distance of the plane from point A to the nearest tenth of a kilometer. 32° 56° 31. Am in Cartesiar fast frequency: 500 Hz, slow and vertical 500 33. Amplitude: 8, fast period: period: 10 slow frequency: 10 Hz 35. D(t)= 20 (0.9086)' coordinate in the pola 3. Determ cos (4nt), 31 second to plot the in the opp CHAPTER 10 is a distan Section 10.1 1. The altitude extends from any vertex to the opposite side or to the line containing the opposite side at a 90° angle. the known values are the side opposite the missing angle and another side and its opposite angle. sides and a non-included angle. polar axis negative then mo point 3 u 3. When negative 5. A triangle with two to an an given 7. B= 72°, a ~ 12.0, positive 9. y= 20°, b2 4.5, c 1.6 down t b~19.9 11. b 3.78 15. One triangle, a 50.3°, ß~ 16.7°, a ~ 26.7 17. Two triangles, y 54.3°, B2 90.7°, b 2 20.9 or y' 125.7°, 13. c 13.70 7. (-5 B' 19.3°, b' 2 6.9 b~9.9 or B'~ 18.3°, y'~ 118.7°, b' ~ 3.2 19. Two triangles, B 75.7°, y~ 61.3°, 13. ( 21. Two triangles, a - 143.2°, ß= 26.8°, a 2 17.3 or a'~ 16.8°, B' 2 153.2°, a' 8.3 19. r 23. No triangle possible 25. A - 47.8° or A' ~ 132.2° 27. 8.6 29. 370.9 31. 12.3 33. 12.2 35. 16.0 25. 37. 29.7° 39. x = 76.9°or x = 103.1° 41. 110.6° 43. A 39.4, C 47.6, BC - 20.7 45. 57.1 47. 42.0 29. 49. 430.2 51. 10.1 53. AD - 13.8 55. AB - 2.8 57. L 49.7, N ~ 56.1, LN 2 5.8 59. 51.4 feet 31. 37. 61. The distance from the satellite to station A is approximately 1,716 miles. The satellite is approximately 1,706 miles above the ground. 71. 24.1 ft 73. 19,056 ft² 75. 445,624 square miles 77. 8.65 ft2 41 63. 2.6 ft 65. 5.6 km 67. 371 ft 69. 5,936 ft 45 Section 10.2 1. Two sides and the angle opposite the missing side. 3. s is the semi-perimeter, which is half the perimeter of the triangle. 5. The Law of Cosines must be used for any oblique (non-right) 9. 34.7 triangle, 7. 11.3 11. 26.7 13. 257.4 15 sible 17. 95.5° 19. 26.9° 21. B 45.9°, 6.4 3. A 20.6°, B 38.4°, c 51.1 2 98.4° 27. 177.56 in? 29. 0.04 m² 39. 70.7° 49. 1.41 35. 29.1 37. 0.5 45. 9.3 47. 43.52 55. 48.98 57. 52° 6. 24.0 km 69. 2,371 miles