Question

31. A tree 12m high, is broken by the storm. The top of the tree touches the ground making an angle 60°. At what height from the bottom the tree is broken​

Answer 1

Given :

• Height of the tree = 12 m.

• Top of the tree touches the ground making = 60 ° angle.

To find :

• What is the height from the bottom, the tree is broken ?

According to the question :

Let the height of the unbroken tree be 'h'

We know that the height of the tree is 12 m,

∴ The height of the tree broken = 12 - h

Solving :

⟹ sin 60 = height / 12 - h

⟹ sin 60 = h / 12 - h

⟹ 12 $\sf\sqrt{3}$ - h $\sf\sqrt{3}$ = 2h

⟹ h = ( 12 $\sf\sqrt{3}$ ) / ( 2 + $\sf\sqrt{3}$ )

⟹ $\sf\sqrt{3}$ = 1.732

⟹ h = 5.569 m

• ∴ The height from the bottom, the tree is broken is 5.569 m.