580 CHAPTER 5 Trigonometric Functions 74. Flying Distance The bearing from A to C is N64° W. The bearing from A to B is S82° W. The bearing from B to C is N 26° E. A plane flying at 350 mph takes 1.8 hr to go from A to B. Find the distance from B to C. 75. Distance between Two Cities The bearing from Winston-Salem, North Carolina, to Danville, Virginia, is N 42° E. The bearing from Danville to Goldsboro, North Carolina, is S 48° E. A car traveling at 65 mph takes 1.1 hr to go from Winston-Salem to Danville and 1.8 hr to go from Danville to Goldsboro. Find the distance from Winston-Salem to Goldsboro. 76. Distance between Two Cities The bearing from Atlanta to Macon is S 27° E, and the bearing from Macon to Augusta is N 63° E. An automobile traveling at 62 mph needs 11 4 hr to go from Atlanta to Macon and 1 3 4 hr to go from Macon to Augusta. Find the distance from Atlanta to Augusta. Solve each problem. See Examples 7 and 8. 77. Height of a Pyramid The angle of elevation from a point on the ground to the top of a pyramid is 35° 30′. The angle of elevation from a point 135 ft farther back to the top of the pyramid is 21° 10′. Find the height of the pyramid. 218 109 358 309 h 135 ft 78. Distance between a Whale and a Lighthouse A whale researcher is watching a whale approach directly toward a lighthouse as she observes from the top of this lighthouse. When she first begins watching the whale, the angle of depression to the whale is 15° 50′. Just as the whale turns away from the lighthouse, the angle of depression is 35° 40′. If the height of the lighthouse is 68.7 m, find the distance traveled by the whale as it approached the lighthouse. x 68.7 m 158 509 358 409 79. Height of an Antenna A scanner antenna is on top of the center of a house. The angle of elevation from a point 28.0 m from the center of the house to the top of the antenna is 27° 10′, and the angle of elevation to the bottom of the antenna is 18° 10′. Find the height of the antenna. 80. Height of Mt. Whitney The angle of elevation from Lone Pine to the top of Mt. Whitney is 10° 50′. A hiker, traveling 7.00 km from Lone Pine along a straight, level road toward Mt. Whitney, finds the angle of elevation to be 22° 40′. Find the height of the top of Mt. Whitney above the level of the road. 81. Find h as indicated in the figure. 82. Find h as indicated in the figure. 168 m 41.2° h 52.5° 392 ft 29.5° h 49.2°
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