# Find the radius, if s=38,000cm theta=45.3^circ Use the arc length formula.

Question
Analytic geometry
s=38,000cm
$$\displaystyle\theta={45.3}^{\circ}$$
Use the arc length formula.

2020-12-29
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

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