solving the triangle

Question

The angle of elevation to the top of a tower from point A on the ground is

15.4°.

From a point​ B,

32.8

feet closer to the​ tower, the angle of elevation is

18.5°.

What is the height of the​ tower?

Answer 1

tan(15.4 degrees) = (tower top height)/x

tan(18.5 degrees) = (tower top height)/(x-33.8 feet)

tower top height = tan(15.4)*x = tan(18.5)*(x-33.8)

tan(15.4)*x = tan(18.5)*x - tan(18.5)*33.8

x = -tan(18.5)*33.8/(tan(15.4)-tan(18.5))

x ≈ 191.1991722916

tower height = x*tan(15.4) ≈ 52.6650263423 feet

Or, rounded to one decimal place, 52.7 feet.

Note: this value can be checked by using the other equation for the tower height.