SECTION 8.1 Right Triangle Trigonometry; Applications 555 57. Finding the Speed of a Truck A state trooper is hidden 30 feet from a highway. One second after a truck passes, the angle θ between the highway and the line of observation from the patrol car to the truck is measured. See the figure. PD 30 ft u 1 sec (a) If the angle measures 15 ,° how fast is the truck traveling? Express the answer in feet per second and in miles per hour. (b) If the angle measures 20 ,° how fast is the truck traveling? Express the answer in feet per second and in miles per hour. (c) If the speed limit is 55 miles per hour and a speeding ticket is issued for speeds of 5 miles per hour or more over the limit, for what angles should the trooper issue a ticket? 58. Security A security camera in a neighborhood bank is mounted on a wall 9 feet above the floor. What angle of depression should be used if the camera is to be directed to a spot 6 feet above the floor and 12 feet from the wall? 59. Parallax One method of measuring the distance from Earth to a star is the parallax method. The idea behind computing this distance is to measure the angle formed between the Earth and the star at two different points in time. Typically, the measurements are taken so that the side opposite the angle is as large as possible. Therefore, the optimal approach is to measure the angle when Earth is on opposite sides of the Sun, as shown in the figure. Earth's orbit Earth at time 1 Earth at time 2 Parallax Star Sun (a) Proxima Centauri is 4.22 light-years from Earth. If 1 light-year is about 5.9 trillion miles, how many miles is Proxima Centauri from Earth? (b) The mean distance from Earth to the Sun is 93,000,000 miles. What is the parallax of Proxima Centauri? 50. Finding the Distance across a Pond Find the distance from A to C across the pond illustrated in the figure. 100 ft B A C 40° 51. The Eiffel Tower The tallest tower built before the era of television masts, the Eiffel Tower was completed on March 31, 1889. Find the height of the Eiffel Tower (before a television mast was added to the top) using the information given in the figure. 80 ft 85.361° 52. Finding the Distance of a Ship from Shore A person in a small boat, offshore from a vertical cliff known to be 100 feet in height, takes a sighting of the top of the cliff. If the angle of elevation is found to be 25 ,° how far offshore is the boat? 53. Finding the Distance to a Plateau Suppose that you are headed toward a plateau 50 meters high. If the angle of elevation to the top of the plateau is 20 ,° how far are you from the base of the plateau? 54. Finding the Reach of a Ladder A 22-foot extension ladder leaning against a building makes a 70° angle with the ground. How far up the building does the ladder touch? 55. Finding the Angle of Elevation of the Sun At 10 am on April 26, 2025, a building 300 feet high cast a shadow 50 feet long. What was the angle of elevation of the Sun? 56. Directing a Laser Beam A laser beam is to be directed through a small hole in the center of a circle of radius 10 feet.The origin of the beam is 35 feet from the circle (see the figure).At what angle of elevation should the beam be aimed to ensure that it goes through the hole? Laser ? 10 ft 35 ft
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