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.


Given:


Angle of elevation of top of a hill at foot of a tower = ∠DBC = 60°


Angle of elevation of top of a tower at foot of a hill = ∠ACB = 30°


Height of the tower AB is 50 m.


Let height of the hill CD be h m.


Consider ΔABC,


⇒ tan30° = AB/BC


⇒ 1/√3 = 50/BC


⇒ BC = 50√3


Consider ΔBCD,


⇒ tan60° = CD/BC


⇒ √3 = h / (50√3)


⇒ h = (50√3) √3


∴ h = 50 × 3 = 150 m


Ans. Height of the hill is 150 m.


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