Degrees: [tex]s = \frac{\pi}{180}\theta r[/tex]
[tex]s = \frac{\pi}{180}(\frac{s}{r})(r)[/tex]
[tex]s = \frac{\pi}{180}(\frac{165}{4})(4)[/tex]
[tex]s = \frac{\pi}{180}(41.25)(4)[/tex]
[tex]s = \frac{\pi}{180}(165)[/tex]
[tex]s = \frac{165\pi}{180}[/tex]
[tex]s = \frac{11\pi}{12}[/tex]
[tex]s = \frac{11\pi}{12} * \frac{180}{\pi}[/tex]
[tex]s = 11 * 15[/tex]
[tex]s = 165\°[/tex]
Radians: [tex]s = \theta r[/tex]
[tex]s = \frac{s}{r}(r)[/tex]
[tex]s = \frac{165}{4}(4)[/tex]
[tex]s =41.25(4)[/tex]
[tex]s =165[/tex]
[tex]s =165 * \frac{\pi}{180}[/tex]
[tex]s =11 * \frac{\pi}{12}[/tex]
[tex]s = \frac{11\pi}{12}[/tex]
[tex]Arc\ Length = \frac{central\ angle}{360} * circumference[/tex]
[tex]Arc\ Length = \frac{\theta}{360} * 2\pi r[/tex]
[tex]Arc\ Length = \frac{165}{360} * 2(3.14)(4)[/tex]
[tex]Arc\ Length = \frac{11}{24} * 2(12.56)[/tex]
[tex]Arc\ Length = \frac{11}{24} * 25.12[/tex]
[tex]Arc\ Length = \frac{276.32}{24}[/tex]
[tex]Arc\ Length \approx 11.51\bar{3}[/tex]
The answer is A.
