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

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

Question
Analytic geometry
asked 2020-12-28
Find the radius, if
s=38,000cm
\(\displaystyle\theta={45.3}^{\circ}\)
Use the arc length formula.

Answers (1)

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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