Question

A ladder $20m$ long reaches a point $20m$ below the top of a flag and makes an angle ${60}^{\circ }$ with the horizontal. Find the length of the flagstaff, in meters

• A. $40$
• B. $20$
• C. $30$
• D. $10(2+\sqrt{3})$

Answer 1

The correct option is D $10(2+\sqrt{3})$

In the above diagram, $AC$ and point $D$ is the top of the flag.

In $△ABC,$

$\begin{array}{cc}\sin {60}^{\circ }& =\frac{BC}{AC}\\ \frac{\sqrt{3}}{2}& =\frac{h}{20}\\ h& =10\sqrt{3}m\end{array}$

So,

$BD=BC+CD$

$=h+20$

$=10\sqrt{3}+20$

$=10(2+\sqrt{3})m$