The length of arc is given by:
[tex]\begin{gathered} l=r\theta \\ where\colon \\ \theta=angle_{\text{ }}(in_{\text{ }}radians) \\ r=radius \end{gathered}[/tex]therefore:
[tex]\begin{gathered} \theta=78=\frac{13}{30}\pi \\ r=9 \\ l=9\cdot\frac{13}{30}\pi \\ l\approx12.25 \end{gathered}[/tex]