Given:
[tex]\begin{gathered} A=13ft^2 \\ r=7.5\text{ ft} \end{gathered}[/tex]The area of a sector is given by
[tex]\begin{gathered} A=\frac{\emptyset}{360^{\circ}}\ast\pi\ast r^2 \\ \text{Here }\emptyset\text{ is the central angle of the sector and r is the radius of circle} \\ \text{The equation can rewritten as} \\ \emptyset=\frac{A}{\pi\ast r^2}\ast360^{\circ} \end{gathered}[/tex]Substitute the given values.
[tex]\begin{gathered} \emptyset=\frac{13}{\pi\ast7.5^2}\ast2\pi \\ \emptyset=\frac{13}{56.25^{}}\ast2=0.46radians\cong0.5\text{ radians} \end{gathered}[/tex]The central angle is 0.5 radians.
