Given:

\(r=3.5ft\)

\(\displaystyle\angle={130}^{\circ}\)

First, find \(\displaystyle\theta\):

\(\displaystyle\theta=\angle\times{\left(\frac{\pi}{{180}^{\circ}}\right)}\)

\(\displaystyle\theta=\frac{{{130}\pi}}{{180}}\)

\(\displaystyle=\frac{{{13}\pi}}{{18}}\)

Use the formula:

\(\displaystyle{s}={r}\theta\)

Where s represents the length of the piece of cloth moved. Substitute:

\(\displaystyle{s}={3.5}\times\frac{{{13}\pi}}{{18}}\)

\(\displaystyle{s}\approx{8}\) ft