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A tree, $15$ m high, is broken by the wind in such a way that its top touches the ground and makes an angle $30^{o}$ with the ground. At what height from the bottom is the tree broken by the wind?

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5

6

7

8

answer is A.

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Detailed Solution

It is given that a tree of height

15

m is broken by the wind in such a way that its top touches the ground and makes an angle

30^{o}

with the ground.
Question Image

Let AB be the height of tree

= 15 m

.
The tree is broken at point C.
The broken part of the tree which touches the ground be CO.
Let

AC = x

and

BC = 15 - x

.
In right

ΔOCA

\sin 30^{0} = \frac{AC}{OC}

⇒

\frac{1}{2} = \frac{x}{15 - x}

⇒

2 x = 15 - x

⇒

3 x = 15

⇒

x = 5

m
The tree is broken at height of

5 m

.
Hence, the correct option is 1.

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