What is the angle of depression in the airplane must use for its descent?

Question

The plane is flying at 5 miles above the ground. The horizontal distance from the airplane to the start of the runway is 19 miles.

Answer 1

This situation can be modeled using a right triangle. Go ahead and draw it. The vertices are the plane, the start of the runway, and a point above the start of the runway level with the plane. That "point above" is the right angle.

 

An angle of depression is the angle you'd have to look downwards to see something. For you, that's the downwards angle of your line of sight if you were standing in the plane and looking at the start of the runway. In other words, we're trying to find the measure of the angle located at the plane. Call it A.

 

Label the length of the leg from the start of the runway to the "point above" as 5 (since the plane is 5 miles high) and label the length of the triangle's other leg, from the plane to the "point above," as 19 (since the plane's horizontal distance from the runway is 19 miles).

 

Since we have the lengths of both legs, we'll use tangent to find the angle of depression, A:

 

tan(A) = opposite/adjacent

tan(A) = 5/19

A = tan^-1(5/19)

A = 14.74 degrees