Question

A tree breaks due to wind and the broken part bends so that the top of the tree touches the ground making an angle of ${60}^o$ with it. The distance between the foot of the tree to the point where the top touches the ground is $9m$. Find the total height of the tree before it was broken.

Answer 1

From figure,

Let say the height of the broken part is $y$ and it touches the ground at $9m$ from the foot.

Height of the tree $=x+y$

Therefore, from the figure:

$tan{60}^o=\frac{x}{9}$

$⟹\sqrt{3}=\frac{x}{9}$

Hence, $x=9\sqrt{3}m$

And, $cos{60}^o=\frac{9}{y}$

$⟹\frac{1}{2}=\frac{9}{y}$

Hence, $y=18m$

So, the height of the tree $=x+y=9(2+\sqrt{3})m$