Question

A tree $12 m$ high, is broken by the wind in such a way that its top touches the ground and makes an angle $60^{\circ}$ with the ground. The height from the bottom of the tree from where it is broken by the wind is approximately

• A. $5.57 m$
• B. $5.21$
• C. $5.36$
• D. $5.9$

Answer 1

Answer: (A)

$\sin 60^{\circ}=\frac{x}{12-x}$
$\frac{\sqrt{3}}{2}=\frac{x}{12-x}$
$12 \sqrt{3}-\sqrt{3} x=2 x$
$x(2+\sqrt{3})=12 \sqrt{3}$
$x=\frac{12 \sqrt{3}}{2+\sqrt{3}} $ x $\frac{2-\sqrt{3}}{2-\sqrt{3}}$

$x=12(2 \sqrt{3}-3)$
$x=12(2 \times 1.732-3)$
$x=12 \times 0.464$
$x=5.568 \,m$