Two men on either side of a pole observe its top at the angles of elevation $45^o$ and $60^o$ respectively and the distance between two men is $48m$, find the height of the pole?

Consider the following question.

Angle of elevation of First man=$45^0$

Angle of elevation of Second man=$60^0$

Distance B/W two man=48m

Let,

BD$=x$

  $\tan {45}^0=\frac{H}{x}$

 $1=\frac{H}{x}$

 $H=x.....\left(1\right)$

 $\tan {60}^0=\frac{H}{x-48}$

 $\sqrt{3}=\frac{H}{x-48}$

 $\sqrt{3}x-48\sqrt{3}=H...\left(2\right)$

Puth the value of eq.(1) in eq.(2), we get.

 $\sqrt{3}H-H=48\sqrt{3}$

 $H\left(\sqrt{3}-1\right)=48$

 $H=\frac{48}{\left(\sqrt{3}-1\right)}m$

Hence, this is the required answer.