The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

NCERT Class X
Mathematics - Mathematics

Chapter _SOME APPLICATIONS OF
TRIGONOMETRY

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2015-06-12T09:20:33+05:30

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Let the distance between the foot of the tower and the foot of the building be d.

height of the building = H
height of the tower = h = 50 m

Tan 30⁰ = 1/√3 = H/d
Tan 60⁰ = √3 = h/d
               =>  (1/√3)/(√3) = H / h
             =>   H  =  h/3  =>   50 m / 3  = 16.667 meters

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