A radio tower stands on the top of a hill that is 85 feet high. From the bottom of the hill, the elevation angle to the base of the tower is 42 degrees and the elevation angle to the top of the tower is 60 degrees. How tall is the tower?

Question

I would like to know what steps to take to arrive at this answer.

Answer 1

Step 1:
Draw a diagram, with a tower of height h on top of a hill 85' hight.
The 42° angle of elevation is measured at a horizontal distance x from the base of the tower.
Step 2:
Calculate x knowing that tan(42)=85/x
Step 3:
Calculate h knowing that
tan(60)=(85+h)/(x)
Step 4:
Solve for h.