A vertically straight tree, 15m height, is broken by the wind in such a way that its top just touches the ground and makes an angle of 60° with the ground. At what height from the ground did the tree break?

Question

A vertically straight tree, 15m height, is broken by the wind in such a way that its top just touches the ground and makes an angle of 60&#xB0; with the ground. At what height from the ground did the tree break?

Philoid · Accepted Answer

Total height of the tree is 15 m.

I.e AB= 15m.

Let height at which tree is broken is h (m)

Therefore BC = h (m)

CD = AB-BC

= 15-h.

In ∆DBC,

sin 60° =

=

On cross-multiplication

√3(15-h) = 2h

⇒ 15√3-√3h = 2h

⇒ h(2+√3) = 15√3

h =

on multiplying and dividing by 2-√3

h =

h = ⇒ ⇒ 6.96 m.

Therefore the tree is broken at 6.96 m from the ground.