#### Question

A tree breaks due to the storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 10 metres. Find the height of the tree.

#### Solution

Let *AB* be the tree of height *h*. And the top of the tree makes an angle of 30° with the ground. The distance between the foot of the tree to the point where the top touches the ground is 10M.

lET bc = 10 And ∠ACB = 30°

Here we have to find the height of the tree.

Here we have the corresponding figure

So we use trigonometric ratios.

In a triangle ABC

`=> tan C = (AB)/(BC)`

`=> tan 30^@ = (AB)/((BC)`

`=> 1/sqrt3 = h/10`

`=> h = 10/sqrt3`

Now in tiangle ABC we have

`sin 30^@ = h/(AC)`

`=> 1/2 = 10/(sqrt3 AC)`

`=> AC = 20/sqrt3`

So the length of the tree is

` = AB + AC`

= h + AC

`= 10/sqrt3 + 20/sqrt3`

`= 10sqrt3`

= 1.73

Hence the height of tree is 17.3 m