Q. 48

A tree standing on a horizontal plane is leaning towards east. At two points situated at distances a and b exactly due west on it, the angles of elevation of the top are respectively α and β. Prove that the height of the top from the ground is

Answer :

In the fig let RP be the leaning tree, R & S be the two points at distance ‘a’ and ‘b’ from point Q.



In ∆PQR


tan θ° =


tan θ° =


x = ………….(1)


In ∆PQS


tan α =


tan α = ……………….(2)


In ∆PQT


tan α =


tan β =


tan β = …………….(3)


On substituting value of x from eqn (1) in eqn (2) we get,


tan α =


h tan α + a tan θ tan α = h tan θ


h tan α = tan θ(h-a tan α)


tan θ = …………….(4)


Now on substituting value of x in eqn (3)


tan β =


Now on substituting value of tan θ in eqn (4)


tan β =


h2tan β = 0


h(h tan β = 0


h()+tan αtan β(b-a) = 0


h = Proved


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