Question

A cellphone tower is located 700 feet from an office building. When looking out the window of the office, the angle of elevation to the top of the tower is 46 degrees, and the angle of depression to the bottom of the tower is 32 degrees. What is the height of the cellphone tower? (Please describe how you found the answer.)

Answer 1

By creating two right triangles (one for depression and one for elevation) and by using 700 as the adjacent side, you can use tangents to find the opposite sides and add them together. 

Tan(45) = opposite side/700 or 700tan(45) = opposite side (elevation). 

This of course equals 700. 

Then do the same for the depression. 

Tan(32) = opposite side/700 or 700tan(32) = opposite side (elevation). 

Which equals 437.4. 

Adding the two together and you get the height of the cell tower at 1137.4ft