Question

Two men standing on opposite sides of a flag staff measure the angles of the top of the flagstaff as ${30}^{\circ }$ and${60}^{\circ }$. If the height of the flagstaff is $18$ $m$ the distance between the men is :

• A. $24$ $m$
• B. $24\sqrt{3}m$
• C. $\frac{24}{\sqrt{3}}m$
• D. $31.2$ $m$

Answer 1

The correct option is B $24\sqrt{3}m$

Let $A$ and $B$ be the points where the two men standing respectively.

Now let angle of elevation of the top of the flag-staff from $A$ be ${60}^o$ and that of, from the point $B$ be ${30}^o$.

Then from $\Delta AOC$

$\tan {60}^o=\frac{OC}{OA}$

$\Rightarrow \tan {60}^o=\frac{18}{OA}$

$\Rightarrow OA=6\sqrt{3}$.....(1).

And, from $\Delta OBC$

$\tan {30}^o=\frac{OC}{OB}$

$\Rightarrow \tan {30}^o=\frac{18}{OB}$

$\Rightarrow OA=18\sqrt{3}$.....(2).

Thus, the distance between the two men is $AB=OA+OB$$=24\sqrt{3}$ $cm$. [Using $\left(1\right)$ and $\left(2\right)$]