Question

A tree, $15$m high, is broken by the wind in such a way that its top touches the ground and makes an angle ${30}^o$ with the ground. At what height from the bottom is the tree broken by the wind?

• A. $5$m
• B. $6$m
• C. $7$m
• D. $8$m

Answer 1

The correct option is A $5$m

Let AB be the height of tree $=15m$.

The tree is broken at point C. The broken part of tree which touches the ground be CO.

$AB=15$, then let $AC=x$ and $BC=15-x$.

In right $\Delta OCA$

$sin{30}^0=\frac{AC}{OC}$

$=>\frac{1}{2}=\frac{x}{15-x}$

$=>2x=15-x$

$=>3x=15$

$=>x=5$m

The tree is broken at height of $5m$