576 CHAPTER 5 Trigonometric Functions 40. Distance across a Lake To find the distance RS across a lake, a surveyor lays off length RT = 53.1m, so that angle T = 32° 10′ and angle S = 57° 50′. Find length RS. 41. Height of a Building From a window 30.0 ft above the street, the angle of elevation to the top of the building across the street is 50.0° and the angle of depression to the base of this building is 20.0°. Find the height of the building across the street. 42. Diameter of the Sun To determine the diameter of the sun, an astronomer might sight with a transit (a device used by surveyors for measuring angles) first to one edge of the sun and then to the other, estimating that the included angle equals 32′. Assuming that the distance d from Earth to the sun is 92,919,800 mi, approximate the diameter of the sun. Sun Earth d NOT TO SCALE 43. Side Lengths of a Triangle The length of the base of an isosceles triangle is 42.36 in. Each base angle is 38.12°. Find the length of each of the two equal sides of the triangle. (Hint: Divide the triangle into two right triangles.) 44. Altitude of a Triangle Find the altitude of an isosceles triangle having base 184.2 cm if the angle opposite the base is 68° 44′. Solve each problem. See Examples 3 and 4. 45. Height of a Tower The shadow of a vertical tower is 40.6 m long when the angle of elevation of the sun is 34.6°. Find the height of the tower. 46. Distance from the Ground to the Top of a Building The angle of depression from the top of a building to a point on the ground is 32° 30′. How far is the point on the ground from the top of the building if the building is 252 m high? 47. Length of a Shadow Suppose that the angle of elevation of the sun is 23.4°. Find the length of the shadow cast by a person who is 5.75 ft tall. 23.48 5.75 ft T R Lake S 30.0 ft 20.08 50.08
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