Question

question 4
20 pts
from an airplane the angle of depression (from the sky)to the runway is 20°. the airplane is at an altitude of 500 ft. what is the ground distance to the runway? round to the nearest tenth if necessary.

Explanation:

Step1: Identify the trig - ratio

We know the angle of depression is \(20^{\circ}\) and the altitude (opposite side) is 500 ft. We want to find the ground distance (adjacent side). We use the tangent function \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

Step2: Set up the equation

Let \(x\) be the ground distance. \(\tan(20^{\circ})=\frac{500}{x}\).

Step3: Solve for \(x\)

We can rewrite the equation as \(x = \frac{500}{\tan(20^{\circ})}\). Since \(\tan(20^{\circ})\approx0.364\), then \(x=\frac{500}{0.364}\approx1373.7\) ft.

Answer:

1373.7 ft