Question

Two men standing on either side of a cliff 90m, high observes the angle of evelation of the top of the cliff to be $30^0$ and $60^0$ respectively. Find the distance between the two men.

Answer 1

- For $1^{st}$ man -for $2^{nd}$ man

$\tan {30}^o=\frac{BD}{AB}$ $\tan {60}^o=\frac{BD}{BC}$

$\frac{1}{\sqrt{3}}=\frac{90}{AB}$ $\sqrt{3}=\frac{90}{BC}$

$AB=90\sqrt{3}$ $BC=\frac{90}{\sqrt{3}}$

Now distance b/w $2$ men.

$AC=AB+BC=90\sqrt{3}+90/\sqrt{3}$

$=90(\sqrt{3}+\frac{1}{\sqrt{3}})$

$=90\left(\frac{3+1}{\sqrt{3}}\right)$

$=\frac{90\times 4}{\sqrt{3}}=207.84$