Answer
$134.7\ cm$
Work Step by Step
Draw a vertical line from top as shown in the figure, half of the top angle is $\frac{68^\circ44'}{2}=34^\circ22'$, we have $tan(34^\circ22')=\frac{184.2/2}{x}$, thus $x=\frac{92.1}{tan(34^\circ22')}\approx134.7\ cm$