To use the formula for radian measure, you must first have the radius and the arc length in the same units, so you must convert one of them.

Now: $\displaystyle{\left(\frac{{{3}\pi}}{{4}}\ \text{ feet}\right)}{\left(\frac{{{1}\ \text{ yard}}}{{{3}\ \text{ feet}}}\right)}=\frac{\pi}{{4}}\ \text{ yards}\usepackage{cmbright}\Huge\$

So: $\displaystyle\theta=\frac{{s}}{{r}}=\frac{{\frac{\pi}{{4}}\ \text{ yd}}}{{\frac{{1}}{{2}}\ \text{ yd}}}=\frac{\pi}{{4}}\cdot\frac{{2}}{{1}}=\frac{\pi}{{2}}\usepackage{cmbright}\Huge\$