Question

A passenger in an airplane flying at an altitude of 37,000 feet sees two towns directly to the west of the airplane. The angles of depression to the towns are 32° and 76°. How far apart are the towns?

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Answer 1

`49,987.24\ ft`

Explanation:

Let

x-----> distance from the two towns

we know that

In the right triangle ABC

`tan(32\°)=37,000/(x+y)\\x+y=37,000/tan(32\°)`

In the right triangle ABD

`tan(76\°)=37,000/(y)\\y=37,000/tan(76\°)`

see the attached figure to better understand the problem

Remember that

(x+y)-y=x

so

`x=(37,000)/(tan(32\°)) -(37,000)/(tan(76\°))`

`x=49,987.24\ ft`