In a triangular plot$ABC$ with $BC = 7 m,$
$CA = 8 m and AB = 9 m$. $A$lamp post is situated at the middle
point $E$of the side $AC$ and subtends an angle ${\tan }^{-1}3$

at the point $B$, the height of the lamp post is

In triangle $ABC$

$a=BC=7,b=CA=8$ and $c=AB=9$

so that $\cos C=\frac{a^2+b^2-c^2}{2ab}=\frac{49+64-81}{2\times 7\times 8}=\frac{2}{7}$

In triangle $BEC,BC=7,CE=4\text{ and }\cos C=\frac{2}{7}$ 

so that $B{E}^2=4^2+7^2-2\times 4\times 7\times \frac{2}{7}=49$

$\Rightarrow BE=7$.

If $h$is the height of the lamp post $EP$ at $E$

then $\frac{PE}{BE}=\frac{h}{7}=\tan \left({\tan }^{-1}3\right)=3\Rightarrow h=21\mathrm{m}.$