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A straight tree breaks due to wind and the broken parts bends

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A straight tree breaks due to wind and the broken parts bends without getting detached such that the top of the tree touches the ground making an angle of 30 $^{o}$ with the ground. The distance from the part of the tree to the point when the top touches the ground is 10 m. The height of the tree is _____.

10(

3

- 1) m

10(

3

+ 1) m

10(

34

- 1) m

10(

3

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A straight tree breaks due to wind and the broken parts bends without getting detached such that the top of the tree touches the ground making an angle of 30

^{o}

with the ground. The distance from the part of the tree to the point when the top touches the ground is 10 m. The height of the tree is _____.

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Text solutionVerified

Refer figure, let AB be the tree broken at point C

such that CD takes position CD and

∠

ADC = 30

^{o}

Then,

A D = 10

m.
Let,

A C = x

m and CD

= y

m
Then the height of the tree

= (x + y)

Now,

\frac{A C}{A D} = tan 3 0^{o} \Rightarrow \frac{x}{10} \Rightarrow x = \frac{10}{3}

And,

\frac{A D}{C D} = cos 3 0^{o} \Rightarrow \frac{3}{2} = \frac{10}{y} \Rightarrow y = \frac{20}{3}

∴

Height of tree

= x + y

\frac{10}{3} + \frac{20}{3}

\frac{30}{3}

m = 10

3

So, option D is correct.

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Question Text	A straight tree breaks due to wind and the broken parts bends without getting detached such that the top of the tree touches the ground making an angle of 30 $^{o}$ with the ground. The distance from the part of the tree to the point when the top touches the ground is 10 m. The height of the tree is _____.
Answer Type	Text solution:1
Upvotes	150

Text solutionVerified

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