SECTION 8.1 Right Triangle Trigonometry; Applications 551 Figure 12 Horizontal (a) Angle of elevation Object Angle of elevation Line of sight Horizontal Object (b) Angle of depression Angle of depression Line of sight If a person is looking down at an object, the acute angle made by the line of sight to the object and the horizontal is called the angle of depression. See Figure 12(b). Finding the Height of a Cloud Meteorologists find the height of a cloud using an instrument called a ceilometer. A ceilometer consists of a light projector that directs a vertical light beam up to the cloud base and a light detector that scans the cloud to detect the light beam. See Figure 13(a). At Midway Airport in Chicago, a ceilometer was employed to find the height of the cloud cover. It was set up with its light detector 300 feet from its light projector. If the angle of elevation from the light detector to the base of the cloud was 75 ,° what was the height of the cloud cover? EXAMPLE 8 Figure 13 (b) 300 ft h 75° u (a) Cloud height h Light projector Base b Light detector Vertical light beam Illuminated spot on base of clouds Solution Figure 13(b) illustrates the situation. To find the height h, use the fact that h tan75 300 , ° = so h 300tan75 1120 feet = ° ≈ The ceiling (height to the base of the cloud cover) was approximately 1120 feet. Now Work PROBLEM 51 The idea behind Example 8 can also be used to find the height of an object that is positioned above ground level. Finding the Height of a Statue on a Building Adorning the top of the Board of Trade building in Chicago is a statue of Ceres, the Roman goddess of wheat. From street level, two observations are taken 400 feet from the center of the building. The angle of elevation to the base of the statue is found to be 55.1 ,° and the angle of elevation to the top of the statue is 56.5 .° See Figure 14(a) on the next page. What is the height of the statue? EXAMPLE 9 (continued)
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