we have the following formula for the area of a sector of a circle:
[tex]A_s=\frac{\theta\cdot\pi}{360}\cdot r^2_{}[/tex]
In this case, we have the following information:
[tex]\begin{gathered} A_s=60\pi \\ \theta=24\degree \end{gathered}[/tex]
then, using the formula and solving for r, we get the following:
[tex]\begin{gathered} 60\pi=\frac{24\cdot\pi}{360}\cdot r^2 \\ \Rightarrow360\cdot60\pi=24\pi\cdot r^2 \\ \Rightarrow21600\pi=24\pi\cdot r^2 \\ \Rightarrow r^2=\frac{21600\pi}{24\pi}=900 \\ \Rightarrow r=\sqrt[]{900}=30 \\ r=30 \end{gathered}[/tex]
therefore, the measure of the radius is r = 30
