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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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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.

Height of transmission tower = AB = AC – BC

AB, Height of the tower

From figure, In right ΔBCD,

tan 45° = \(\frac{BC}{CD}\)

1 = \(\frac{20}{CD}\)

CD = 20

In right ΔACD,

tan 60° = AC/CD

√3 = \(\frac{AC}{20}\)

AC = 20√3

AB = AC – BC = (20√3 - 20)

= 20(√3 - 1)

Height of transmission tower = 20(√3 – 1) m.

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