Question

A tree breaks due to storm and the broken part bends so that the top of the trees touches the ground making an angle ${30}^o$ with ground. The distance between the foot of the tree to the point where the top touches the ground is $8m$. Find the height of the tree.

• A. 18 m
• B. 5 m
• C. $\sqrt{3}$
• D. 8$\sqrt{3}$m

Answer 1

The correct option is D 8$\sqrt{3}$m

Let the length of the broken part be l.
And the length of the portion still standing (the length from the foot of the tree till where it broke) be h.
Hence
$\sin {30}^0=\frac{h}{l}$
Hence
$h=l\sin {30}^0$
$l=2h$ ...(i)
And
$\tan {30}^0=\frac{h}{8}$
$h=8\tan {30}^0$
$h=\frac{8}{\sqrt{3}}m$
Hence total length is
$h+l$
$=3h$
$=8\sqrt{3}m$