Question

A vertically straight tree, 12m high is broken by the wind in such a way that its top touches the ground and make an angle of 60° with the ground. at what height from the ground the tree is broken by the wind

Answer 1

See the attach file for ur ans

Answer 2

Answer:

5.5692 m

Step-by-step explanation:

Refer the attached figure

The height of the tree  AB = 12 m

Let BC be x

So, AC = AB - BC = 12-x

Now, AC = CD=12-x

Its top touches the ground and make an angle of 60° with the ground.i.e.∠CDB = 60°

In ΔBCD

$\frac{BC}{CD} = sin 60^{\circ}$

$\frac{x}{12-x} =\frac{\sqrt{3}}{2}$

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

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

$2x+\sqrt{3}x =12\sqrt{3}$

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

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

$x =5.5692$

So, the height above the ground from the tree broke is 5.5692 m