SECTION 8.1 Right Triangle Trigonometry; Applications 557 75. Finding the Pitch of a Roof A carpenter is preparing to put a roof on a garage that is 20 feet by 40 feet by 20 feet. A steel support beam 46 feet in length is positioned in the center of the garage. To support the roof, another beam will be attached to the top of the center beam (see the figure). At what angle of elevation is the new beam? In other words, what is the pitch of the roof? New beam 46 ft 20 ft 40 ft 10 ft 20 ft ? 76. Shooting Free Throws in Basketball The eyes of a basketball player are 6 feet above the floor. The player is at the freethrow line, which is 15 feet from the center of the basket rim (see the figure). What is the angle of elevation from the player’s eyes to the center of the rim? [Hint: The rim is 10 feet above the floor.] 10 ft 15 ft ? 6 ft 77. Geometry Use the figure below to find the value of the angle θ in degrees rounded to the nearest tenth of a degree. 4 2 u 71. Mt. Rushmore To measure the height of Lincoln’s caricature on Mt. Rushmore, two sightings 800 feet from the base of the mountain are taken. If the angle of elevation to the bottom of Lincoln’s face is 32° and the angle of elevation to the top is 35 ,° what is the height of Lincoln’s face? 72. The CN Tower The CN Tower, located in Toronto, Canada, is the tallest structure in the Americas. While visiting Toronto, a tourist wondered what the height of the tower above the top of the Sky Pod is. While standing 4000 feet from the tower, she measured the angle to the top of the Sky Pod to be 20.1 .° At this same distance, the angle of elevation to the top of the tower was found to be 24.4 .° Use this information to determine the height of the tower above the Sky Pod. Credit: MasterPhoto/Shutterstock 73. Chicago Skyscrapers The angle of inclination from the base of the John Hancock Center to the top of the main structure of the Willis Tower is approximately 10.3 .° If the main structure of the Willis Tower is 1451 feet tall, how far apart are the two skyscrapers? Assume the bases of the two buildings are at the same elevation. Source: www.emporis.com 74. Estimating the Width of the Mississippi River A tourist at the top of the Gateway Arch (height, 630 feet) in St. Louis, Missouri, observes a boat moored on the Illinois side of the Mississippi River 2070 feet directly across from the Arch. She also observes a boat moored on the Missouri side directly across from the first boat (see figure). Given that B cot 67 55 , 1 = − estimate the width of the Mississippi River at the St. Louis riverfront. Source: U.S. Army Corps of Engineers Boat Boat IL MO 630 ft 2070 ft A B
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