Question

Can someone please answer. There is one problem. There's a picture. Thank you!

Answer 1

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.

Answer 2

$\dfrac{165^o}{360^o}=\dfrac{11}{24}\\\\Circumference\ of\ the\ circle:C=2\pi r\\\\r=4\to C=2\pi\cdot4=8\pi\\\\|\widehat{CT}|=\dfrac{11}{24}\cdot8\pi=\dfrac{11}{3}\pi\approx11.51\\\\Answer:\boxed{11.51}$