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A tree breaks due to a storm and the broken part bends down such that the top of the tree touches the ground making an angle of $30^{o}$ with the ground at a distance of $30$ m. Then, the height of the tree is,

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35

\sqrt{3}

60

\sqrt{3}

45

\sqrt{3}

30

\sqrt{3}

answer is D.

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Detailed Solution

Given that,
Angle =

30^{o}

The distance between the top and the bottom of the tree = 30m
Question Image

We have to find the height of the tree.
Let AB be the tree broken at point C.
The broken part CB takes the position CO and touches the ground at O. OA = 30 m

∠

COA =

30^{o}

We have the formula,

tanθ = \frac{Height}{Distance}

△

OAC,
tan

30^{o}

\frac{AC}{OA}

\Rightarrow \frac{1}{\sqrt{3}} = \frac{AC}{30}

\Rightarrow AC = \frac{30}{\sqrt{3}}

\Rightarrow AC = 10 \sqrt{3}

m
cos

30^{o}

\frac{OA}{OC}

\Rightarrow \frac{\sqrt{3}}{2} = \frac{30}{OC}

\Rightarrow OC = \frac{60}{\sqrt{3}}

\Rightarrow OC = 20 \sqrt{3}

m
The height of the tree will be,

h = AC + CB

\Rightarrow h = AC + OC

.... (

∵

BC = OC)

\Rightarrow h = 10

\sqrt{3}

+ 20

\sqrt{3}

\Rightarrow h = 30

\sqrt{3}

m
Thus, the height is

30

\sqrt{3}

m.
Therefore, the correct option is 4.

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