Q20 of 47 Page 1

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


Let hill be AB and tower be CD


Given: Height of the tower = 50 m


Hence, CD = 50 m


Angle of elevation of top of tower from the foot of a hill = 30°


Hence, ∠ CBD = 30°


Angle of elevation of top of the hill at the foot of tower = 60°


Hence, ∠ ADB = 60°


Now, In right ΔCBD, we have




⇒BD = 50√3


In right ΔADB, we have




⇒ h = (50√3) × (√3)


⇒ h = 150 m


Hence, the height of the hill is 150m


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