570 CHAPTER 5 Trigonometric Functions EXAMPLE 4 Finding an Angle of Depression From the top of a 210-ft cliff, David observes a lighthouse that is 430 ft offshore. Find the angle of depression from the top of the cliff to the base of the lighthouse. SOLUTION As shown in Figure 50, the angle of depression is measured from a horizontal line down to the base of the lighthouse. The angle of depression and angle B, in the right triangle shown, are alternate interior angles whose measures are equal. We use the tangent ratio to solve for angle B. tan B = side opposite side adjacent Tangent ratio tan B = 210 430 Side opposite = 210; side adjacent = 430 B = tan-1a 210 430b Use the inverse tangent function. B ≈26° Two significant digits S Now Try Exercise 49. 210 ft 430 ft A C B Angle of depression Figure 50 Bearing We now investigate problems involving bearing, a term used in navigation. Bearing refers to the direction of motion of an object, such as a ship or airplane, or the direction of a second object at a distance relative to the ship or airplane. We introduce two methods of measuring bearing. Expressing Bearing (Method 1) When a single angle is given, it is understood that bearing is measured in a clockwise direction from due north. Several sample bearings using Method 1 are shown in Figure 51. Figure 51 N 328 N 1648 N 2298 N 3048 Bearings of 32°, 164°, 229°, and 304° CAUTION A correctly labeled sketch is crucial when solving applications like those that follow. Some of the necessary information is often not directly stated in the problem and can be determined only from the sketch.
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