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The height of a tower is 300 meters. When its top is seen from top of another tower, then the angle of elevation is 60°. The horizontal distance between the bases of the two towers is 120 metres. What is the height (in metres) of the small tower?

The height of a tower is 300 meters. When its top is seen from top of another tower, then the angle of elevation is 60°. The horizontal distance between the bases of the two towers is 120 metres. What is the height (in metres) of the small tower? Correct Answer 92.15

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let height of the small tower be x

DB = CE = x

ED = CB = 120

AD = AB - DB = 300 - x

In triangle AED

tan 60 = AD/ED

√3 = (300 - x)/120

∴ x = 300 - 120√3 = 92.15 metres

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