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### Height of the Plane

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Date: 03/29/2001 at 13:54:29
From: Peter Komorowski
Subject: Pre-Calculus

Question: Towers A and B are known to be 4.1 mi. apart on level
ground. A pilot measures the angles of depression to the towers to be
36.5 degrees and 25 degrees, respectively. Find the height of the
airplane.

I tried to answer this question and simply did not have any idea how
to do it.
```

```
Date: 03/29/2001 at 17:02:06
From: Doctor Jaffee
Subject: Re: Pre-Calculus

Hi Peter,

A good picture can be very helpful in solving a problem like this one.

Draw line PQ, where P and Q represent the bases of the two towers and
the length of the segment PQ is 4.1 miles.

Then draw line AB parallel to line PQ. Point A represents the location
of the airplane. Point A should be situated so that the measure of
angle BAQ is 25, and the measure of angle BAP is 36.5.

Finally, locate point C on line PQ so that AC is perpendicular to PQ.

Now you should be able to calculate the measures of all the angles in
the drawing fairly easily, and then use the Law of Sines in triangle
APQ to calculate the length of AP. Once you know that, you should be
able to work in triangle ACP and calculate AC, the height of the
airplane.

Give it a try and if you want to check your answer with me or if you
need more help, write back.

- Doctor Jaffee, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Trigonometry

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