Question

A man standing at a point $P$ is watching the top of a tower 10 m in height, which makes an angle of elevation of ${30}^o$ with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation ${45}^o$. What is the distance between the base of the tower and the point $P$?

Answer 1

Let the angle of elevation ${30}^{\circ }$

Height of tower $=10m$

And the distance of point $P$ from base of tower let $D$

Now,

$\tan \theta =\frac{perpendicular}{base}$

$\tan {30}^{\circ }=\frac{10}{D}$

$D=10\sqrt{3}$