Technical Mathematics, Sixth Edition

7.3. Applications of the Right Triangle

There are, of course, a huge number of applications for the right triangle, a few of which are given in the following examples and exercises. A typical application is that of finding a distance that cannot be measured directly, as shown in the following example.

Example 12: To find the height of a flagpole (Fig. 7-16), a person measures 35.0 ft from the base of the pole and then measures an angle of 40.8° from a point 6.00 ft above the ground to the top of the pole. Find the height of the flagpole. Estimate: If angle A were 45°, then BC would be the same length as AC, or 35 ft. But our angle is a bit less than 45°, so we expect BC to be less than 35 ft, say, 30 ft. Thus our guess for the entire height is about 36 ft. Solution: In right triangle ABC, BC is opposite the known angle, and AC is adjacent. Using the tangent, we get where x is the height of the pole above the observer. Then x = 35.0 tan 40.8° = 30.2 ft Adding 6.00 ft, we find that the total pole height is 36.2 ft, measured from the ground.

Figure 7.16. FIGURE 7-16

Example 13: From a plane at an altitude of 2750 ft, the pilot observes the angle of depression of a lake to be 18.6°. How far is the lake from a point on the ground directly beneath the plane? Figure 7.17. Angles ...