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