If an observer stands at a certain point in the same horizontal plane as the base of a radio tower. the angle of elevation of the top of the tower is 13deg 15'. If the observer moves 156.25 feet towards the tower, the angle of elevation is 18deg 10'. Find the height of the tower.

Answer 1

Tan13.25 = h/(X+156.25)
h = (X+156.25)*Tan13.25
h = 0.23547x + 36.79

Tan18.17 = h/X
h = 0.32820x

h = 0.23547x + 36.79 = 0.32820x
0.23547x - 0.32820x = -36.79
-0.09273x = -36.79
X = 396.7 Ft.

Tan18.17 = h/396.7
h = 396.7*Tan18.17 = 130.2 Ft = Ht. 0f
tower.