Q. 104.4( 18 Votes )

A person observed the angle of elevation of the top of a tower as 30°. He walked 50 m towards the foot of the tower along level ground and found the angle of elevation of the top of the tower as 60°. Find the height of the tower.

Answer :


Let the height of the tower = h (m)


In ∆ABD,


tan 60° =


√3 =


h = ---------- (1)


In ∆ABC,


tan 30° =


tan 30° =


------(2)


on substituting value of h from equn. (1) In equn. (2)



On cross multiplication


√3×√3 =


3 =


3


2


25 m.


Now substituting value of in eqn. (1)


h = 25√3 43.3m.


Therefore height of tower is 43.3 m.


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