Two men on either side of a cliff $\displaystyle 75$ m high observe the angles of elevation of the top of the cliff to be $\displaystyle 30$° and $\displaystyle 60$°. Find the distance between the two men. Fig.

\[\begin{aligned} \tan 30^{\circ}=\frac{1}{\sqrt{3}} & =\frac{75}{A C} \\ \Rightarrow A C & =75 \sqrt{3} \mathrm{~m} \ldots \ldots \ldots \text { (i) } \\ \tan 60^{\circ} & =\sqrt{3}=\frac{75}{A D} \\ \Rightarrow & A D=25 \sqrt{3} \text { m... ... ... (ii) } \end{aligned} \] Adding (i) and (ii) \[\begin{aligned} C D & =(75 \sqrt{3}+25 \sqrt{3}) \mathrm{m} \\ & =100 \sqrt{3} \mathrm{~m} \end{aligned} \]