Question

A pilot can see the runway she is about to land on directly ahead. When looking at each end of the runway, the angles of depression are 45° and 42°. If the airplane is 1,500 ft. off the ground, how long is the runway?

Create an equation to model the problem. Then solve the equation.

Answer 1

A pilot can see the runway she is about to land on directly ahead. When looking at each end of the runway, the angles of depression are 45° and 42°. If the airplane is 1,500 ft. off the ground, how long is the runway?
Create an equation to model the problem. Then solve the equation.


165.92 ft.

Answer 2

First, we get the length of the runway in which the pilot had seen a 45° by using the trigonometric formula of tangent.
tan 45° = 1,500 / x
The value of x from the equation is 1500 ft.
We do the same for the 42°
tan 42° = 1,500 / y
The value of y is equal to 1665.92 ft. To determine the length of the runway, we subtract the lengths calculated and this will give us an answer of 165.92 ft.