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

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

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)=(9,000)/(x),\\x=(9,000)/(\tan 16^(\circ)),\\x\approx \boxed{31,387\:\text{ft}}`.