Answer
$B = 28.125^\circ \hspace{10pt} C =39.675^\circ \hspace{10pt} c =30.2\, cm$
Work Step by Step
$\sin{B} = \dfrac{b \sin{A}}{a} = \dfrac{22.3 \times \sin{122.2^\circ}}{43.8}$
$\sin{B} = 0.471$
$B = 28.125^\circ \hspace{40pt} B' = 180-B = 151.875^\circ$
$A+B' = 264.075^\circ > 180^\circ \hspace{10pt} \therefore B'$ is refused.
$C = 180-(A+B) = 39.675^\circ$
$c = \dfrac{a \sin{C}}{\sin{A}} = \dfrac{43.8 \times \sin{39.675}}{\sin{112.2}} = 30.2 \, cm$