Question

a tree breaks due to storm and the broken part bends so that the top of the tree touches the ground by making 30 degree angle with the ground. the distance between the foot of the tree and the top of the tree on the ground is 6 m. find the height of the tree.

Answer 1

This attachment is required answer.

Answer 2

Given,

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground by making 30 degree angle with the ground.

The distance between the foot of the tree and the top of the tree on the ground is 6 m.

To find out,

The height of the tree.

Solution:

Let AB be remaining part of the tree after broken = h meters.

C be the point of observation on the ground.

AC be the distance between the foot of the tree and the top of the tree on the ground = 6 meters.

Now,

$In \: \triangle \: ABC$

$\tan30 \degree = \frac{opposite \: side \: to \: 30 \degree}{adjacent \: side \: to \: 30 \degree}$

$\frac{1}{ \sqrt{3} } = \frac{h}{6}$

$h = \frac{1}{ \sqrt{3} } \times 6$

$h = \frac{6}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} }$

$h = \frac{6 \sqrt{3} }{3}$

$h = 2 \sqrt{3}$

Now,We have to find out the hypotenuse.

$\sin30 \degree = \frac{opposite \: side \: to \: 30 \degree \: }{hypotenuse}$

$\frac{1}{2} = \frac{2 \sqrt{3} }{x}$

$x = 4 \sqrt{3}$

The part of tree which was bent by the strom is 4√3 meters.

Height of tree = Broken part + remaing

$Height \: of \: tree = 4 \sqrt{3} + 2 \sqrt{3}$

$Height \: of \: tree = 6 \sqrt{3}$

Therefore the height of the tree is 6√3 meters.