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.


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