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

`\alpha =107.4^(o)`

Explanation:

`15=(\pi (8)\alpha )/(180)`

`\alpha =((15)(180))/(8\pi ) =(2700)/(25.13)=107.4`

Hope this helps