At a certain distance, the angle of elevation to the top of a building is 60°. From 40 feet further back, the angle of elevation is 45°. Find the height of the building.
Let H be the height of the bldg and D be the original distance from the buildng
So
tan 60 = H / D
cot 60 = D /H
H cot 60 = D
And we have that
tan 45 = H / ( D + 40)
1 = H / ( D + 40)
D + 40 = H
H cot 60 + 40 = H
40 = H ( 1 - cot 60)
40 / (1 - cot 60) = H ≈ 94.64 ft
