Question

To approach the runway, a pilot of a small plane must begin a 5 degree descent starting from a height of 1407 feet above the ground. To the nearest tenth of a mile, how many miles from the runway is the airplane at the start of this approach?

Answer 1

3.0 miles

Explanation:

The tangent of the angle relates the opposite side (altitude) to the adjacent side (distance to runway):

tan(5°) = (altitude)/(distance to runway)

Then we have ...

distance to runway = (1407 ft)/(tan 5°) ≈ 16,082 ft

In miles, that is ...

distance to runway = (16082 ft)/(5280 ft/mi) = 3.0458 mi

The pilot is 3.0 miles from the runway at the start of his approach.