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. Draw a sketch of this situation (you do not need to submit the sketch). Find the ground distance from Charlie to the plane. Type your answer below. Explain your work.

Answer 1

Check the picture.

Let the given points represent the following:

F : Charlie's feet
E: Charlie's eyes
P: location of the plane
G: the foot of the perpendicular drawn from P to the ground
A: a point on PG, such that |GA|=|FE|=5.2 feet.

Clearly EAP is a right triangle, with m(AEP)=32°, side PA=1,700-5.2=1694.8 feet.

the ground distance from Charlie to the plane is |FG|=|EA|

from right angle trigonometry, we know that:

$tan32= \frac{PA}{AE}$

$0.625= \frac{1694.8}{AE}$

$AE= \frac{1694.8}{0.625}=2711.68$ feet


Answer: 2711.68 feet