Question

1. air traffic from the top of the 120-foot-high tower, an air traffic controller observes an airplane on the runway at an angle of depression of 19°. how far from the base of the tower is the airplane? round to the nearest tenth of a foot.

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the height of the tower (120 ft) is the opposite side to the angle of depression (which is equal to the angle of elevation from the airplane to the top of the tower, 19°), and the distance from the base of the tower to the airplane (let's call it \( x \)) is the adjacent side. So we use the tangent function: \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \)
\( \tan(19^\circ) = \frac{120}{x} \)

Step2: Solve for \( x \)

Rearrange the formula to solve for \( x \): \( x = \frac{120}{\tan(19^\circ)} \)
Calculate \( \tan(19^\circ) \approx 0.3443 \)
Then \( x = \frac{120}{0.3443} \approx 348.5 \)

Answer:

348.5