Hello, mathbuoy!

Did you make a sketch?

Two towers with heights and meters are 100 meters apart.

What is the height of the intersection point of the lines

joining the top of each tower to the base of the other? Code:

P *
|*
| *
| *
| *
| *
a | * * R
| *T * |
| * |
| * | | b
| * h| * |
| * | *|
Q * - - - * - * S
100-x U x

The towers are: .

The lines cross at , .

Let

Since .[1]

Since .[2]

Equate [1] and [2]: .

Substitute into [1]: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

An observation . . .

Divide top and bottom by

The answer is one-half the *harmonic mean* of