Question

Find the angle of this sector. on the image ​

Answer 1

$\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ s=15\\ r=8 \end{cases}\implies 15=\cfrac{\theta \pi (8)}{180}\implies 15=\cfrac{2\pi \theta }{45} \\\\\\ 675=2\pi \theta \implies \cfrac{657}{2\pi }=\theta \implies 104.56^o\approx \theta =a$

Answer 2

Answer:

$\alpha =107.4^{o}$

Step-by-step explanation:

$15=\frac{\pi (8)\alpha }{180}$

$\alpha =\frac{(15)(180)}{8\pi } =\frac{2700}{25.13}=107.4$

Hope this helps