Correct. The arc determined by $\displaystyle\angle{P}{O}{Q}\usepackage{cmbright}\Huge\$ has length $\displaystyle{s}={1}\frac{{1}}{{3}}\usepackage{cmbright}\Huge\$ feet. The radius $\displaystyle{r}={4}\usepackage{cmbright}\Huge\$ inches. You need to have the two measurements in the same units, so you must convert one of them:

$\displaystyle{s}={1}\frac{{1}}{{3}}\ \text{ ft}=\frac{{4}}{{3}}\ \text{ ft}\cdot\frac{{{12}\ \text{ in}}}{{{1}\ \text{ ft}}}=\frac{{48}}{{3}}\ \text{ in}={16}\ \text{ in}\usepackage{cmbright}\Huge\$

Now substitute these lengths into the formula: $\displaystyle\theta=\frac{{s}}{{r}}=\frac{{{16}\ \text{ in}}}{{{4}\ \text{ in}}}={4}\usepackage{cmbright}\Huge\$