The angle of elevation of the top of water tower from point

The angle of elevation of the top of water tower from point A the ground is 19.9 degree. From Point B, 50.0 feet closer to the tower, the angle of elevation is 21.8 degree. what is the height of the tower to the nearest foot? Show work to receive credit.

Solution

Let h be the height of the tower and x be the distance from the base of the tower to point A.

tan19.9 = h/x
tan21.8 = h/(50 - x)

0.362 = h/x
0.362x = h

0.400 = h/(x - 50)
0.400(x - 50) = h
0.400x - 20 = h

0.400x - 20 = 0.362x
0.038x = 20
x = 20/0.038
x = 526.3ft

tan19.9 = h/x
0.362 = h/526.3
526.3(0.362) = h
h = 190.5ft

The water tower is 190.5 feet high.