Question

A tree is broken by the wind. Its top struck the ground at an angle ${30}^o$ at a distance of $30m$ from its foot. The whole height of the tree is:

• A. $10\sqrt{3}m$
• B. $20\sqrt{3}m$
• C. $40\sqrt{3}m$
• D. $30\sqrt{3}m$

Answer 1

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

From figure,

In $△ABC$

$\tan 30=\frac{BC}{AB}=\frac{1}{\sqrt{3}}$

$\therefore BC=\frac{30}{\sqrt{3}}$

$\cos 30=\frac{AB}{AC}=\frac{\sqrt{3}}{2}$

$\therefore AC=\frac{60}{\sqrt{3}}$

Total height,

$=BC+AC$

$=\frac{30}{\sqrt{3}}+\frac{60}{\sqrt{3}}$

$=30\sqrt{3}m$