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From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.

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Let BC be the 20 m high building.
D is the point on the ground from where the elevation is taken.
Height of transmission tower = AB = AC - BC

In  right ΔBCD,

tan 45° = BC/CD
⇒ 1 = 20/CD
⇒ CD = 20 m

In  right ΔACD,

tan 60° = AC/CD
⇒ √3 = AC/20

⇒ AC = 20√3 m
Height of transmission tower = AB = AC - BC = (20√3 - 20) m = 20(√3 - 1) m.

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