Question

A tree $9$m high is broken by the wind & its top touches the ground and makes an angle ${30}^o$ with the ground. At what height from the bottom the tree is broken by the wind?

• A. $6$m
• B. $10$m
• C. $3$m
• D. $7$m

Answer 1

The correct option is C $3$m

Let ACB be the total length of the tree broken $AC+BC=9m$

Let height of $BC=h$m

Then $CD=CA=9-h$

$\sin {30}^{\circ }=\frac{BC}{CA}$

$\frac{1}{2}=\frac{h}{9-h}$

$2h=9-h$

$2h+h=9$

$3h=9$

$\therefore h=3m$

Hence at 3 m from the bottom the tree is broken.