$\begin{aligned} & \text { } \tan \mathrm{c}=\frac{3 \sqrt{5}}{2} \\ & \Rightarrow \cos \mathrm{C}=\frac{2}{7} \\ & \cos \mathrm{c}=\frac{\mathrm{a}^2+\mathrm{b}^2-\mathrm{c}^2}{2 \mathrm{ab}} \\ & \Rightarrow \frac{2}{7}=\frac{49+64-\mathrm{c}^2}{2.7 .8} \\ & \Rightarrow 32=113-\mathrm{c}^2 \\ & \Rightarrow \mathrm{c}^2=113-32=81 \\ & \Rightarrow \mathrm{c}=9\end{aligned}$