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: Define trigonometric relationship

We use the tangent function, where $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 19^\circ$, opposite side = 120 ft, adjacent side = distance $x$ we need to find.

Step2: Rearrange to solve for $x$

$x = \frac{120}{\tan(19^\circ)}$

Step3: Calculate the value

First, find $\tan(19^\circ) \approx 0.3443$, then $x \approx \frac{120}{0.3443}$

Answer:

348.5 feet