Question

An airplane is sighted at the same time by two ground observers who are 2 miles apart and both directly west of the airplane. They report the angles of elevation at 14 degrees and 20 degrees. How high is the airplane?

A.1.58
B.2.24
C.0.68
D.0.48

Answer 1

To solve this problem you must apply the proccedure shown below:

1. You have that the two ground observersare 2 miles apart They report the angles of elevation at 14 degrees and 20 degrees.

2. Therefore, you have:

h: the height of the airplane.

Tan(20°)=h/x
h=xTan(20°)

Tan(14°)=h/(x+2)
h=(x+2)Tan(14°)

xTan(20°)=(x+2)Tan(14°)
x=4.34

3. The height is:

h=xTan(20°)
h=4.34(Tan(20°))
h=1.58

The answer is: A. 1.58

Answer 2

We can conclude that the correct answer is A.1.58
Check the procedures in the attached picture.