The angle of elevation of the top of a building from a point on the level ground is twice the angle of elevation of a window one-third of the way up the building. find the angle of elevation of the top of the building.

Solution:

          tan 2θ = x/h = 2 tan θ/(1 - tan2 θ)

          tan θ = 2x/3h

          x/h = 2 tan θ/(1 - tan2 θ) = (4x/3h) * 3h/√(9h2 - 4x2)

        (9h2 - 4x2) = 4 h2   

           4x2 =5h2

             x = √5h/2

         tan θ = 2x/3h= √5/3

            θ = 36.70