The length of an arc of a circle is given by the formula:
[tex]\begin{gathered} L\text{ = }\frac{\theta}{360}\times2\pi r \\ \theta\text{ = 2. 5 radians} \\ r\text{ = 10 inches} \end{gathered}[/tex]We need to convert 2. 5 radians to degrees
[tex]\begin{gathered} 1\text{ radian =}\frac{180}{\pi} \\ 2.5\text{ radians =}\frac{180}{\pi}\times2.5=\frac{450}{\pi} \end{gathered}[/tex][tex]\begin{gathered} \text{ Therefore, L =}\frac{450}{360\pi}\times2\pi\times10 \\ L=25\text{inches} \end{gathered}[/tex]Therefore, the length of the arc is 25inches.
