You may have figured out that this is a $\displaystyle{{30}}^{\circ}-{{60}}^{\circ}-{{90}}^{\circ}\usepackage{cmbright}\Huge\$ triangle and set up the correct equation:

$\displaystyle\frac{{p}}{{8}}={\cos{{M}}}={{\cos{{30}}}}^{\circ}=\frac{\sqrt{{3}}}{{2}}\usepackage{cmbright}\Huge\$

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