Let's use the law of sines in order to find the angle A:
[tex]\begin{gathered} \frac{a}{sin(A)}=\frac{b}{sin(B)} \\ so: \\ \frac{10.79}{sin(A)}=\frac{8.75}{sin(11.7)} \end{gathered}[/tex]Solve for A:
[tex]\begin{gathered} A=sin^{-1}(\frac{10.79\cdot sin(11.7)}{8.75}) \\ A\approx14.48 \end{gathered}[/tex]Now, we can find the angle C using the triangle sum theorem:
[tex]\begin{gathered} A+B+C=180 \\ 14.48+11.7+C=180 \\ 26.18+C=180 \end{gathered}[/tex]Solve for C:
[tex]\begin{gathered} C=180-26.18 \\ C\approx153.82 \end{gathered}[/tex]Finally, let's find c using the law of sines again:
[tex]\begin{gathered} \frac{b}{sin(B)}=\frac{c}{sin(C)} \\ so: \\ \frac{8.75}{sin(11.7)}=\frac{c}{sin(153.82)} \end{gathered}[/tex]Solve for c:
[tex]\begin{gathered} c=\frac{8.75\cdot sin(153.82)}{sin(11.7)} \\ c\approx19.04 \end{gathered}[/tex]Answer:
A = 14.48
C = 153.82
c = 19.04
