Calculus Question

Question

From a point level with the base of a water tower, the angle of elevation to the bottom of the water tank is 38° and to the top of the water tank is 47°. If the water tank itself is 20 feet high, what is the height of the tower and tank together? 

I got 37 feet.

Answer 1

If you draw the two triangles, you see that 20 ft is the difference in their heights. The base is the same, so we can write

base (tan(47) - tan(38)) = 20 ft

solve for base = 68.709 ft

Now you can solve for the total height by calculating base * tan(47) = (I get 73.68 ft)