Question

Charlie is at a small airfield watching for the approach of a small plane with engine trouble. He sees the plane at an angle of elevation of 32. At the same time, the pilot radios Charlie and reports the plane’s altitude is 1,700 feet. Charlie’s eyes are 5.2 feet from the ground.

Find the ground distance from Charlie to the plane. Show how you know.

Answer 1

Tan (32°) = 1700 feet / x => x = 1700 feet / tan(32°) = 1700 feet / 0.625 = 2720 feet.

Answer 2

2711.8 ft

Explanation:

We know the horizontal and vertical distances here:

vertical distance = 1,700 feet. In the right triangle formed by the horiz. and vert. distances and the hypotenuse, 1,700 ft is the side opposite the 32° angle of elevation of the plane. We need to know the horiz. distance (ground distance).

The tangent function involves both the horiz. and the vert. distances:

tan Ф = opp / adj

and we can solve this for adj:

opp

adj = ------------

tan Ф

In this case we have:

1700 ft 1700 ft

adj = -------------- = -------------- = 2720.6 ft

tan 32° 0.625

If we take into account the fact that Charlie's eyes are 5.2 ft from the ground, the problem solution becomes:

(1700-5.2) ft 1694.8 ft

adj = -------------------- = ----------------- = 2711.8 ft

tan 32° 0.625