You may have figured out that this is a $\displaystyle{{45}}^{\circ}-{{45}}^{\circ}-{{90}}^{\circ}\usepackage{cmbright}\Huge\$ triangle and set up the correct equation:

$\displaystyle\frac{{8}}{{n}}={\sin{{M}}}={{\sin{{45}}}}^{\circ}=\frac{\sqrt{{2}}}{{2}}\usepackage{cmbright}\Huge\$

At this point, however, you solved the equation incorrectly.