A)
recall that there are 180° in π radians.
[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\[-0.5em] \hrulefill\\ s=10\\ r=5 \end{cases}\implies 10=5\theta \implies \cfrac{10}{5}=\theta \implies \stackrel{\textit{radians}}{2=\theta } \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ x&2 \end{array}\implies \cfrac{180}{x}=\cfrac{\pi }{2}\implies 360=x\pi \\\\\\ \cfrac{360}{\pi }=x\implies 114.59\approx x[/tex]
B)
[tex]\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\[-0.5em] \hrulefill\\ r=5\\ \theta =2 \end{cases}\implies A=\cfrac{(2)(5)^2}{2}\implies A=25[/tex]
