Question

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A tree 12m high is broken by the wind in such a way that its top touches the ground and makes an angle of 60o with the ground. At what height from bottom the tree is broken by the wind. Give the answer to the second place of decimal​

Answer 1

Step-by-step explanation:

Solution: Image result for A tree 12 m high is broken by the wind in such a way that its top touches the ground and makes an angle 60 with the ground. At what height from the bottom the tree is broken by the wind?

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this Answer is copy from Google

Answer 2

Given:-

• Height of tree is 12 m.
• Angle of elevation is 60°.

To find:-

• Height from bottom the tree is broken by the wind.

Solution:-

Let,

AB be the tree of height 12 m. Suppose the tree is broken by the wind at point C. The part CB assumes the position CO and meets the ground at O.

Let AC = x , CO = CB = 12-x.

It is given that ∠AOC = 60°.

In ∆OAC,

$\implies \sf sin \: 60 \degree = \dfrac{AC}{OC}$

$\implies \sf \dfrac{ \sqrt{3} }{2} = \dfrac{x}{12 - x}$

• Cross multiple.

$\implies \sf 12 \sqrt{3} - \sqrt{3} x = 2x$

$\implies \sf 12 \sqrt{3} = x(2 + \sqrt{3} )$

$\implies \sf x = \dfrac{12 \sqrt{3} }{2 + \sqrt{3} }$

• Rationalise the denominator.

$\implies \sf x = \dfrac{12}{2 + \sqrt{3} } \times \dfrac{2 - \sqrt{3} }{2 - \sqrt{3} }$

$\implies \sf x = 12 \sqrt{3} (2 - \sqrt{3})$

$\implies \sf x = 24 \sqrt{3} - 36$

$\implies \sf x = 5.569$

Hence,

The tree is broken at a height of 5.56 m from the ground.