558 CHAPTER 8 Applications of Trigonometric Functions spire is 34 .° The angle of elevation from the helipad on the roof of the office building to the tip of the spire is 20 .° 348 208 1776 (a) How far away is the office building from One World Trade Center? Assume the side of the tower is vertical. Round to the nearest foot. (b) How tall is the office building? Round to the nearest foot. 81. Challenge Problem Drive Wheel of an Engine The drive wheel of an engine is 13 inches in diameter, and the pulley on the rotary pump is 5 inches in diameter. If the shafts of the drive wheel and the pulley are 2 feet apart, what length of belt is required to join them as shown in the figure? 2.5 in. 6.5 in. 2 ft 82. Challenge Problem Rework Problem 81 if the belt is crossed, as shown in the figure. 2.5 in. 6.5 in. 2 ft 78. Surveillance Satellites A surveillance satellite circles Earth at a height of h miles above the surface. Suppose that d is the distance, in miles, on the surface of Earth that can be observed from the satellite. See the figure. (a) Find an equation that relates the central angle θ to the height h. (b) Find an equation that relates the observable distance d and .θ (c) Find an equation that relates d and h. (d) If d is to be 2500 miles, how high must the satellite orbit above Earth? (e) If the satellite orbits at a height of 300 miles, what distance d on the surface can be observed? d h u 3960 3960 79. Calculating Pool Shots A pool player located at X wants to shoot the white ball off the top cushion and hit the red ball dead center. He knows from physics that the white ball will come off a cushion at the same angle as that at which it hit the cushion. If the deflection angle, ,θ is 52 ,° where on the top cushion should he hit the white ball? 3 ft X u u 1 ft 80. One World Trade Center One World Trade Center in New York City is 1776 feet tall (including its spire). The angle of elevation from the base of an office building to the tip of the 117 feet high on a hill 245 feet high, so its beam of light is 362 feet above sea level. A brochure states that ships 40 miles away can see the light and planes flying at 10,000 feet can see it 120 miles away.Verify the accuracy of these statements. What assumption did the brochure make about the height of the ship? 83. Explain how you would measure the width of the Grand Canyon from a point on its ridge. 84. Explain how you would measure the height of a TV tower that is on the roof of a tall building. 85. The Gibb’s Hill Lighthouse, Southampton, Bermuda In operation since 1846, the Gibb’s Hill Lighthouse stands Explaining Concepts
RkJQdWJsaXNoZXIy NjM5ODQ=