Hello purplesky828

Welcome to Math Help Forum! Originally Posted by

**purplesky828** ...2. From the top of a tower 60 feet tall the angle of elevation of the top of a building is 14 degrees. From the base of the tower, the angle of elevation of the tops of the building is 28 degrees. How far is the tower from the building and how high is the building?

This is very similar to number 1. Let the distance from the foot of the tower to the foot of the building be $\displaystyle d$ feet, and let the height of the tower be $\displaystyle h$ feet.

Draw a diagram, marking in all the distances and the two angles. (Can you do that?)

Then you have two right angled triangles. From one you get:

$\displaystyle \tan14^o = \frac{h-60}{d}$

and from the other, you get:

$\displaystyle \tan28^o = \frac{h}{d}$

Then you need to:

- eliminate $\displaystyle d$ between these two equations;

- solve the resulting equation for $\displaystyle h$;

- substitute back to find $\displaystyle d$.

Can you complete it now?

Grandad