Math CentralQuandaries & Queries


Question from joyce, a student:

The angle of elevation of tower B from the top of tower A is 28 degrees and the angle of elevation of the top of tower A from the base is 46 degrees.

Find the height of tower A if tower B is 120 m high?

Hi Joyce.

I drew a diagram of the problem on the right.

We want AE.
We know DB = 120m, CBA = 28°, ADE = 46°.

First, note that AE = AB tan 46°. Also, AE = CD.

Now, note that BC = AC tan 28°. Also AC = AB.

Thus, DB = AB tan 46° + AB tan 28° = 120m.

Solve for AB. Use this to solve for AE in our earlier equation.

Hope this helps,
Stephen La Rocque.

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