556 CHAPTER 8 Applications of Trigonometric Functions shows the path that they decide on and the measurements taken. What is the length of highway needed to go around the bay? US 41 3 mi 1 mi 1408 1308 68. Photography A camera is mounted on a tripod 4 feet high at a distance of 10 feet from George, who is 6 feet tall. See the figure. If the camera lens has angles of depression and elevation of 20 ,° will George’s feet and head be seen by the lens? If not, how far back will the camera need to be moved to include George’s feet and head? 208 208 6' 10' 4' 69. Finding the Distance between Two Objects A blimp, suspended in the air at a height of 500 feet, lies directly over a line from Soldier Field to the Adler Planetarium on Lake Michigan (see the figure). If the angle of depression from the blimp to the stadium is 32° and from the blimp to the planetarium is 23 ,° find the distance between Soldier Field and the Adler Planetarium. Lake Michigan Adler Planetarium Soldier Field 238 328 500 ft 70. Hot-Air Balloon While taking a ride in a hot-air balloon in Napa Valley, Francisco wonders how high he is. To find out, he chooses a landmark that is to the east of the balloon and measures the angle of depression to be 54 .° A few minutes later, after traveling 100 feet east, the angle of depression to the same landmark is determined to be 61 .° Use this information to determine the height of the balloon. 60. Parallax See Problem 59. The star 61 Cygni, sometimes called Bessel’s Star (after Friedrich Bessel, who measured the distance from Earth to the star in 1838), is a star in the constellation Cygnus. (a) 61 Cygni is 11.14 light-years from Earth. If 1 light-year is about 5.9 trillion miles, how many miles is 61 Cygni from Earth? (b) The mean distance from Earth to the Sun is 93,000,000 miles. What is the parallax of 61 Cygni? 61. Washington Monument The angle of elevation of the Sun is 35.1° at the instant the shadow cast by the Washington Monument is 789 feet long. Use this information to calculate the height of the monument. 62. Finding the Length of a Mountain Trail A straight trail with an inclination of 17° leads from a hotel at an elevation of 9000 feet to a mountain lake at an elevation of 11,200 feet. What is the length of the trail? 63. Finding the Bearing of an Aircraft A Boeing 737 aircraft leaves Midway Airport from runway 4 RIGHT, whose bearing is N40 E. ° After flying for 1 2 mile, the pilot requests permission to turn 90° and head toward the southeast. The permission is granted. After the airplane goes 1 mile in this direction, what bearing should the control tower use to locate the aircraft? 64. Finding the Bearing of a Ship A ship leaves the port of Miami with a bearing of S80 E° and a speed of 15 knots.After 1 hour, the ship turns 90° toward the south. After 2 hours, maintaining the same speed, what is the bearing to the ship from port? 65. Niagara Falls Incline Railway Situated between Portage Road and the Niagara Parkway directly across from the Canadian Horseshoe Falls, the Falls Incline Railway is a funicular that carries passengers up an embankment to Table Rock Observation Point. If the length of the track is 51.8 meters and the angle of inclination is 36 2, ° ′ determine the height of the embankment. Source: www.niagaraparks.com 66. Willis Tower Willis Tower is the tallest building in Chicago and is topped by a high antenna. A surveyor on the ground makes the following measurements: • The angle of elevation from his position to the top of the building is 34 .° • The distance from his position to the top of the building is 2595 feet. • The distance from his position to the top of the antenna is 2760 feet. (a) How far away from the (base of the) building is the surveyor located? (b) How tall is the building? (c) What is the angle of elevation from the surveyor to the top of the antenna? (d) How tall is the antenna? Source: Council on Tall Buildings and Urban Habitat 67. Constructing a Highway A highway whose primary directions are north–south is being constructed along the west coast of Florida. Near Naples, a bay obstructs the straight path of the road. Since the cost of a bridge is prohibitive, engineers decide to go around the bay.The figure
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