Two men on either side of a tower $60$ metres high observe the angle of elevation of the top of the tower to be ${45}^o$ and ${60}^o$ respectively. Find the distance between the two men.

Let the distance of the first man from the foot of the tower be x.
Let the distance of the second man from the foot of the tower be y.
Hence applying trigonometric ratios, we get

$\tan 45^0=\frac{60}{x}$
Hence
$x=60m$
Similarly
$\tan 60^0=\frac{60}{y}$
Hence
$y=20\sqrt{3}$
Therefore the distance between both men will be 
$x+y$
$=20\sqrt{3}(1+\sqrt{3})m$
$=94.64m$