Two men on the same side of a tall building notice the angle of elevation to the top of the building to be 30o and 60o respectively. If the height of the building is known to be h =120 m, find the distance (in meters) between the two men.

Answer 1

Assuming that both observers are at an elevation level with the base of the building.
Height of the building, H = 120m
Distance of observer 1 = D1
Angle of elevation = α
By the definition of tangent = opp/adj
H/D1=tan(α), therefore
D1=H/tan(α)
Since H and α are known, D1 can be calculated numerically.

Distance of observer 2 = D2
Angle of elevation = β
H/D2=tan(β)
D2=H/tan(β)

Distance between observers = D2-D1