Hello, batman121!

A vertial pole stands on the horizontal ground.

A man stands east of the pole and measures the elevation of the top as 45°.

He moves due south 40 meters and it measures 42°.

What is the height of the pole? His first sighting looks like this:

Code:

P *
| *
| *
h | *
| *
| 45° *
Q * - - - - - * A
h

The man is at .The pole is:

He sights the top of the pole and finds

He moves 40 m south.

*Looking down at the ground*, the diagram looks like this: Code:

h
Q * - - - - - * A
* |
* | 40
* |
* B

Using Pythagorus: .

Consider the triangle Code:

P *
| *
| *
h | *
| *
| 42° *
Q * - - - - - - - - * B
√(h² + 40²)

We have: .

Square both sides: .

. .

Hence: .

Therefore: .