We're given:

s=38,000cm

\(\displaystyle\theta={45.3}^{\circ}\)

First, convert \(\displaystyle\theta\) from degrees to radians:

\(\displaystyle\theta={45.3}^{\circ}\times\frac{{\pi}}{{{180}^{\circ}}}\)

\(\displaystyle=\frac{{{45.3}\pi}}{{180}}\)

The arc length formula:

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

Where r=radius. Since that's what we need to find, isolate it:

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

Substitute s and \(\displaystyle\theta\):

\(\displaystyle{r}=\frac{{{38},{000}{\left({180}\right)}}}{{{45.3}\pi}}\)

\(\displaystyle{r}\approx{48062.7}\) cm

s=38,000cm

\(\displaystyle\theta={45.3}^{\circ}\)

First, convert \(\displaystyle\theta\) from degrees to radians:

\(\displaystyle\theta={45.3}^{\circ}\times\frac{{\pi}}{{{180}^{\circ}}}\)

\(\displaystyle=\frac{{{45.3}\pi}}{{180}}\)

The arc length formula:

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

Where r=radius. Since that's what we need to find, isolate it:

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

Substitute s and \(\displaystyle\theta\):

\(\displaystyle{r}=\frac{{{38},{000}{\left({180}\right)}}}{{{45.3}\pi}}\)

\(\displaystyle{r}\approx{48062.7}\) cm