Question

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

Answer 1

I hope it will help you

I think it Anwer should be 5.6 m

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Answer 2

Given :

Height of the tree = 12 m

Angle made by the tree with the ground = 60°

To Find :

At what height from the bottom, the tree is broken by the wind

Solution :

When the wind breaks the tree, a right-angled triangle is formed.

Let 'P' be the perpendicular and 'H' be the Hypotenuse of right-angled triangle having angle 60°.

As per question,

     P + H = 12 m   -------- (i)

We know,

     sin∅    = $\frac{Perpendicular}{Hypotenuse}$

⇒  sin60  = $\frac{P}{H}$

⇒   $\frac{\sqrt{3} }{2}$       =  $\frac{P}{H}$

∴   H        = ( $\frac{2}{\sqrt{3} }$ ) × P

Putting the value of H in equation (i)

⇒  ( $\frac{2}{\sqrt{3} }$ ) × P  + P  = 12

⇒   P($\frac{2}{\sqrt{3} }$ + 1)         = 12

⇒   P($\frac{2 + \sqrt{3} }{\sqrt{3} }$)          = 12

⇒      P                = $\frac{12\sqrt{3} }{2 + \sqrt{3} }$

⇒      P                = $\frac{12\sqrt{3} (2 - \sqrt{3}) }{(2 + \sqrt{3})(2 - \sqrt{3} ) }$

⇒      P                = $\frac{24\sqrt{3} - 36}{4 - 3}$

⇒      P                = 24×1.732 - 36

⇒      P                =  41.568 - 36

∴       P                = 5.568 m

Therefore, the height from where the tree broken is 5.568 m.