A window in a building is at a height of 10 m from the ground. The angle of depression of a point P on the ground from the window is 30˚. The angle of elevation of the top of the building from the point P is 60˚. Find the height of the building.
Let us consider this situation by a diagram as shown, in which AB is a building and C depicts the window and A be the top.
Now Given,
Height of window from the ground, BC = 10 m
Angle of depression of point P from window, ∠XCP = 30°
⇒ ∠XCP = ∠CPB = θ1 = 30° [Alternate Angles]
Angle of elevation of top of the building from point P, ∠APB = 60°
⇒ ∠ APB = θ2 = 60°
Now, In Δ BCP
Cross – Multiplying we get,
BP=10√3 meters
Now, In ΔABP
⇒ AB = 10√3 × √3 = 30 meters
So, Height of building is 30 meters.