Question

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

Answer 1

The height of broken part of tree from ground is 5.569m.

Justification:

Let BD is a tree of height 12 m.

Suppose it got bent at a point C and let the part CD take the position CA, meeting the ground at A.

i.e., CD = AC = h m

Broken part makes 60° angle from ground

So, ∠BAC = 60°

Now, height of remaining part of tree = (12 – h)m.

In right angled ∆ABC,

sin 60° = BC/AC

⇒ √3/2 = (12 - h)/h

⇒ √3h = 2(12 – h)

⇒ √3h = 24 – 2h

⇒ √3h + 2h = 24

⇒ h(√3 + 2) = 24

⇒ h(1.732 + 2) = 24

⇒ h(3.732) = 24

⇒ h = 24/3.732 = 6.4308 m

Hence, height of broken tree from ground

⇒ BC = 12 – h

⇒ 12 – 6.4308 = 5.569m

Hence, tree is broken 5.569 m from ground.

Note: See attached picture.