Q30 of 46 Page 1

The angle of elevation of the top of a hill at the foot of a tower is 60 � and the angle of depression from the top of the tower of the foot of the hill is 30 �. If the tower is 50 m high, find the height of e hill.

We have


Let height of the hill be H m, and distance between the hill and the tower is x m


We shall find value of x first so that we can find H.


In ∆ABC,


[∵, ]


⇒ [∵, tan 30° = 1/√3]


⇒ x = 50√3


Now in ∆DCB,


[∵, ]


⇒ √3 = H/x [∵, tan 60° = √3]


⇒ x√3 = H


⇒ √3 × 50√3 = H [∵, x = 50√3]


⇒ H = 50 × 3 = 150


Hence, the height of hill is 150 m.


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