Answer :

Given that a vertical flag staff of height h is surmounted on a vertical tower of height H(say),


such that FP = h and FO = H.


The angle of elevation of the bottom and top of the flag staff on the plane is PRO = α and FRO = β respectively.



In ∆PRO, we have





And in ∆FRO, we have




Comparing eq. 1 and eq. 2,



Solving for H,


H tan β = (h+H) tan α


H tan β H tan α = h tan α


H (tan β tan α) = h tan α



Hence, proved.


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