You may have used the wrong trigonometric function or made an error in solving your equation.

Refer to a $\displaystyle{{30}}^{\circ}-{{60}}^{\circ}-{{90}}^{\circ}\usepackage{cmbright}\Huge\$ triangle and use the definition of cosine with the given triangle to obtain:

$\displaystyle\frac{{c}}{{7}}={{\cos{{30}}}}^{\circ}=\frac{\sqrt{{3}}}{{2}}\usepackage{cmbright}\Huge\$

Solve this equation for c.