Answer
433 ft
Work Step by Step
In triangle ABC,
$\tan 49.2^{\circ}=\frac{h}{x}$ or $h=x\tan49.2^{\circ}$
In triangle BCD,
$\tan29.5^{\circ}=\frac{h}{x+392}$ or
$h=(x+392)\tan 29.5^{\circ}$
Equating both expressions for $h$, we get
$x\tan49.2^{\circ}=(x+392)\tan29.5^{\circ}$
Using distributive property, we have
$x\tan49.2^{\circ}=x\tan29.5^{\circ}+392\tan29.5^{\circ}$
$\implies x(\tan 49.2^{\circ}-\tan29.5^{\circ})=392\tan29.5^{\circ}$
Or $x=\frac{392\tan29.5^{\circ}}{\tan49.2^{\circ}-\tan29.5^{\circ}}$
We saw above that $h=x\tan49.2^{\circ}$
Substituting for $x$, we get
$h=(\frac{392\tan29.5^{\circ}}{\tan49.2^{\circ}-\tan29.5^{\circ}})\tan49.2^{\circ}$
$=433\,ft$
