Answer
$C = 27.13^\circ \hspace{10pt} C' = 152.87^\circ \hspace{10pt} a = 7.63 \,$ inches
Work Step by Step
$\sin{C} = = \dfrac{c\sin{B}}{b} =\dfrac{3.48 \sin{62.667}}{6.78}$
$\sin{C} = 0.456$
$C = 27.13^\circ \hspace{40pt} C' = 152.87^\circ \hspace{10pt} $(Refused)
$A = 180-(B+C) = 90.203$
$a = \dfrac{b \sin{A}}{\sin{B}} = \dfrac{6.78 \times \sin{90.203}}{\sin{62.667}}$
$a = 7.63 \,$ inches