From a point P on level ground, the angle of elevation of the top of a tower is 27°10'. From a point 23.0 meters closer to the tower and on the same line with P and the base of the tower, the angle of elevation of the top is 51°30'. Approximate the height of the tower. (Round your answer to the nearest tenth.)

Answer 1

If the height is h, and P is x m from the base,

h/x = tan 27°10' = .5132
h/(x-23) = tan 51°30' = 1.2572

rearranging things a bit,

h = .5132x = 1.2572(x-23)
x = 38.8651
so, h = 19.9456, or 19.9m

Answer 2

22.5[39/3m]