Using the law of sines, we would have that:
[tex]\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]
Solving for C,
[tex]\begin{gathered} \frac{b}{\sin B}=\frac{c}{\sin C}\rightarrow\frac{\sin C\cdot b}{\sin B}=c\rightarrow\sin C\cdot b=c\cdot\sin B \\ \\ \rightarrow\sin C=\frac{c\cdot\sin B}{b}_{}\rightarrow C=\sin ^{-1}(\frac{c\cdot\sin B}{b}_{}) \end{gathered}[/tex]
Plugging in the data given,
[tex]\begin{gathered} C=\sin ^{-1}(\frac{(10.3)\cdot\sin (58.8)}{(10.5)}_{}) \\ \\ \Rightarrow C=57 \end{gathered}[/tex]
Therefore, we can conclude that:
