Answer
448 m
Work Step by Step
In triangle ABC,
$\tan 52.5^{\circ}=\frac{h}{x}$ or $h=x\tan52.5^{\circ}$
In triangle BCD,
$\tan41.2^{\circ}=\frac{h}{x+168}$ or
$h=(x+168)\tan 41.2^{\circ}$
Equating both expressions for $h$, we get
$x\tan52.5^{\circ}=(x+168)\tan41.2^{\circ}$
Using distributive property, we have
$x\tan52.5^{\circ}=x\tan41.2^{\circ}+168\tan41.2^{\circ}$
$\implies x(\tan 52.5^{\circ}-\tan41.2^{\circ})=168\tan41.2^{\circ}$
Or $x=\frac{168\tan41.2^{\circ}}{\tan52.5^{\circ}-\tan41.2^{\circ}}$
We saw above that $h=x\tan52.5^{\circ}$
Substituting for $x$, we get
$h=(\frac{168\tan41.2^{\circ}}{\tan52.5^{\circ}-\tan41.2^{\circ}})\tan52.5^{\circ}$
$=448\,m$
