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A tree breaks due to a storm and the broken part bends down su

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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:

35

3

60

3

45

3

30

3

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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:

14 mins ago

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Text solutionVerified

Let AB be the tree broken at point C such that

the broken part CB takes the position CO and touches the at O.

Then, OA = 30 m &

∠

COA = 30

^{o}

△

OAC, tan 30

^{o}

\frac{A C}{O A} \Rightarrow \frac{1}{3} = \frac{A C}{30} \Rightarrow A C = \frac{30}{3} = 103

and,
cos 30

^{o}

\frac{O A}{OC} \Rightarrow \frac{3}{2} = \frac{30}{OC} \Rightarrow OC = \frac{60}{3} \Rightarrow OC = 203

Thus, the height of the tree

= A C + CB

= A C + OC

.... (

∵

BC = OC)

= 10

3

+ 20

3

= 30

3

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Question Text	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:
Answer Type	Text solution:1
Upvotes	150