Question

A tree is broken by the wind. The top struck the ground at an angle of ${30}^{\circ }$ and at a distance of 30 m from the root, then the whole height of the tree. $(\sqrt{3}=1.73)$ is 51.9 m
If true then enter $1$ and if false then enter $0$

• A. 1

Answer 1

The correct option is A 1
Angle made by the broken part with ground = ${30}^{\circ }$
broken tree is at distance (d) = 30 m from the roots
Let broken part be of length = b
and unbroken part of length = u
Now, the broken part, ground and the unbroken part of the tree forms a right angled triangle
Thus, $\tan 30=\frac{u}{d}$
$u=\frac{30}{\sqrt{3}}$
$u=10\sqrt{3}$
$\sin 30=\frac{u}{b}$$

$\frac{1}{2}=\frac{10\sqrt{3}}{b}$

$b=20\sqrt{3}$
Thus, length of tree = $u+b$ = $10\sqrt{3}+20\sqrt{3}=30\sqrt{3}=51.96$ m