Question

Choose the correct answer from the alternatives given.
A tree is broken by the wind. If the top of the tree struck the ground at an angle of ${30}^{\circ }$ and at a distance of 30 m from the root, then the height of the tree is

• A. $15\sqrt{3}m$
• B. $20\sqrt{3}m$
• C. $25\sqrt{3}m$
• D. $30\sqrt{3}m$

Answer 1

The correct option is D $30\sqrt{3}m$

In $\Delta$ ABC,
$tan{30}^{\circ }=\frac{BC}{AB}$
$\Rightarrow BC=30\times \frac{1}{\sqrt{3}}=10\sqrt{3}$m
and $cos{30}^{\circ }=\frac{AB}{AC}$
$\Rightarrow AC=\frac{AB}{\sqrt{3}/2}=\frac{2\times 30}{\sqrt{3}}=20\sqrt{3}$
Height of the tree = BA = BC + CA
= 10$\sqrt{3}+10\sqrt{3}=30\sqrt{3}$m.