Question

From the top of the 140-foot high tower, an air traffic controller observes an airplane on the runway at an angle of depression of 18°.

18°
140 ft
How far is it from the base of the tower to the airplane? Round your answer to the nearest tenth of a foot.

Answer 1

Explanation:

The angle of depression is the downward angle the air traffic controller

looks down from in the tower. It also equals the angle of elevation which is the angle formed by the runway and the line of sight.

With this information you can find the remaining angle:

180 - (90 + 18)

180 - 108 = 72

Let Angle B = 72°

Angle A = 18°

Angle C =90°

We have one side - 140 feet - this is side a - it is across from angle A.

There is a right triangle formed by the runway (side b) the tower, side a, and the line of sight (side c)

Using the law of sines:

sin A/a = sinB/b

sin 18°/a = sin72°/b

.3090/140 = .9510/x

cross multiply and then divide

140 × .9510/.3090

133.14/.3090

430.873 ft

round to a tenth = 430.9 ft