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The angle of elevation of the top of a tower at a point A on t

Question

The angle of elevation of the top of a tower at a point $A$ on the ground is $30^{o}$ . On walking $20$ metres towards the tower, the angle of elevation is $60^{o}$ . Find the height of the tower.

83

103

53

None of these

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Evelyn Discussed

The angle of elevation of the top of a tower at a point

A

on the ground is

30^{o}

. On walking

20

metres towards the tower, the angle of elevation is

60^{o}

. Find the height of the tower.

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Text solutionVerified

Given

Let

BC = x

⟹ A C = 20 + x

From

Δ BC D

tan 60 = \frac{C D}{x}

C D = 3 x \dots (1)

From

Δ A C D

tan 30 = \frac{C D}{x + 20}

C D = \frac{1}{3} (x + 20) \dots (2)

From

(1) & (2)

⟹ 3 x = \frac{1}{3} (x + 20)

⟹ 3 x = x + 20

⟹ 2 x = 20

⟹ x = 10

From

(1)

Height of tower is

3 x

⟹ 103

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Question Text	The angle of elevation of the top of a tower at a point $A$ on the ground is $30^{o}$ . On walking $20$ metres towards the tower, the angle of elevation is $60^{o}$ . Find the height of the tower.
Answer Type	Text solution:1
Upvotes	150