An engineer sees that the angle of elevation to a vertical tower is 45 degrees. When he moves 40 feet closer to the tower on the same straight, level path, he sees that the angle of elevation becomes 55 degrees. How tall is the tower?

Answer 1

Tan 45 = h/d1
h = d1*Tan45

Tan55 = h/(d1-40)
h = (d1-40)*Tan55

h = d1*Tan45 = (d1-40)*Tan55
d1*1 = (d1-40)*Tan55
Divide both sides by Tan55:
0.7d1 = d1-40
0.3d1 = 40
d1 = 133.3 Ft.

h = d1*Tan45 = 133.3 * 1 = 133.3 Ft.