One way to set up a correct equation is to use the definition of cosine:

$\displaystyle{{\cos{{48}}}}^{\circ}=\frac{{y}}{{10}}\usepackage{cmbright}\Huge\$

Solve this equation for y:

$\displaystyle{y}={10}\cdot{{\cos{{48}}}}^{\circ}\approx{10}\cdot{\left({0.6691}\right)}={6.691}\usepackage{cmbright}\Huge\$

This rounds to 6.69.