Question

From the top of a building 60m. high the angles of depression of the top

and the bottom of a tower are observed to be 300

and 600

. Find the height

of the tower.​

Answer 1

Correct Question:

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From the top of a building 60m high the angle of depression of the top and the bottom of a tower are observed to be 30° and 60°. Find the height of the tower.

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Answer:

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Height of the tower is 40 m.

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Explanation:

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In ∆ DEB,

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$\tan30 \degree \: = \frac{60 - h}{x} = \frac{1}{ \sqrt{3} } \\ \\ </p><p></p><p>$

$\implies \: x = \sqrt{3} (60 - h) \: \: \: \: - - (1)$

In ∆ ABC,

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tan 60° = 60/x

$\implies$ √3 = 60/x

$\implies$ x = 60/√3

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Now keeping the value of x in equation 1. We get,

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60/√3 = √3(60 – h)

$\implies$ 60/3 = 60 – h

$\implies$ h = 60 – 20

$\implies$ h = 40

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Thus, height of the tower is 40 m.