Answer
$C=62^{\circ}$
$a=199.5$
and
$b=241.5$
Work Step by Step
I. Need to find the last angle.
$50^{\circ}+68^{\circ}+\angle C=180^{\circ}$
$\implies \angle C=62^{\circ}$
II. Use law of sines formula to find $a$ and $b$
$\dfrac{\sin 50^{\circ}}{a}=\dfrac{\sin 68^{\circ} }{b}=\dfrac{\sin 62^{\circ} }{230}$
This implies that
$a=\dfrac{230 \sin 50^{\circ} }{\sin 62^{\circ}}=199.5$
and
$b=\dfrac{230 \sin 68^{\circ} }{\sin 62^{\circ}}=241.5$
