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The angle of elevation of the top of a hill at the foot of the tower is 45° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If the tower is 60m high, what will  be the height of the hill?

The angle of elevation of the top of a hill at the foot of the tower is 45° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If the tower is 60m high, what will  be the height of the hill? Correct Answer 60√3 m

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Let height of the hill be x m

Distance between hill and tower = y m

According to problem,

⇒ tan45° = x/y

⇒ x = y        ----(1)

According to problem,

⇒ tan30° = 60/y

⇒ 1/√3 = 60/y

⇒ y = 60√3

From (1) we get,

⇒ x = y = 60√3

∴ Height of the hill = 60√3 m

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