You may have figured out that this is a $\displaystyle{{45}}^{\circ}-{{45}}^{\circ}-{{90}}^{\circ}\usepackage{cmbright}\Huge\$ triangle, but then set up your equation incorrectly. One equation that you can use to find the value of p is:

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