Question

A man 2m high observes the angle of elevation to the top of a building to be 61 degrees, and the angle of depression to the bottom of the building to be 18 degrees. How tall is the building?

Answer 1

I've included a picture to illustrate.

We can see from the picture that we need to find side X of the triangle to be able to find side Y of the building.
$tan18= \frac{2}{X} \\ X= \frac{2}{tan18} \\ X=6.16 m$

Now just find side Y:
$tan61=\frac{Y}{6.16}\\ 6.16tan61=Y\\ 11.11m=Y$

Don't forget to add 2 m to 11.11 m for the total height of the building.

13.11 m is the height of the building.