From the given information, we need to find the radius of the circle. The area sector formula given by
[tex]A=\frac{1}{2}r^2\text{ }\theta[/tex]
where A is the sector area, r is the radius of the circle and theta is the central angle in radians.
By substituting the given values into the formula, we have
[tex]89=\frac{1}{2}r^2\cdot\frac{\pi}{5}[/tex]
which is equivalen to
[tex]89=\frac{1}{10}\pi r^2[/tex]
Then, by multiplying both sides by 10, we have
[tex]890=\pi\cdot r^2[/tex]
and by dividing both sides by Pi, we get
[tex]\begin{gathered} \frac{890}{\pi}=r^2 \\ \text{or equivalently,} \\ \frac{890}{3.1416}=r^2 \end{gathered}[/tex]
which gives
[tex]\begin{gathered} 283.2951=r^2 \\ or\text{ equivalently,} \\ r^2=283.2951 \end{gathered}[/tex]
Finally, by taking square root to both sides, we have
[tex]r=\sqrt[]{283.2951}[/tex]
so, the radius is
[tex]r=16.83\text{ meters}[/tex]
Therefore, the answer is option C
