Question

A pilot spots the airport at an angle of depression of 16°. The plane is flying at an altitude of 9,000 ft. What is the ground distance (distance along the ground) from the plane to the airport to the nearest foot

Answer 1

Answer:

$31,387\:\text{ft}$

Step-by-step explanation:

We can form a right triangle using the plane, the airport, and ground and use basic trig for a right triangle to solve this problem.

In a right triangle, $\tan\theta=\frac{\text{opp}}{\text{adj}}$. Therefore, we have the following equation, where $x$ is ground distance between the plane and the airport:

$\tan 16^{\circ}=\frac{9,000}{x},\\x=\frac{9,000}{\tan 16^{\circ}},\\x\approx \boxed{31,387\:\text{ft}}$.