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A tree $9$ m high is broken by the wind and its top touches the ground and makes an angle $30^{o}$ with the ground. At what height from the bottom the tree is broken by the wind?

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6

10

3

7

answer is C.

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Detailed Solution

It is given that a tree

9

m high is broken by the wind and its top touches the ground and makes an angle

30^{o}

with the ground.
Question Image

Let ACB be the total length of the tree broken.
⇒

AC + BC = 9 m

Let height of

BC = h

m.
⇒

CD = CA = 9 - h

In △ ABC,

\sin 30^{\circ} = \frac{BC}{CA}

⇒

\frac{1}{2} = \frac{h}{9 - h}

⇒

2 h = 9 - h

⇒

2 h + h = 9

⇒

3 h = 9

∴ h = 3 m

At 3 m from the bottom the tree is broken.
Hence, the correct option is 3.

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