1 Answer

Mwangi · Answer 1 · 2023-02-02T16:33:57+0000

From the given information, we need to find the radius of the circle. The area sector formula given by

$A=(1)/(2)r^2\text{ }\theta$

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

$89=(1)/(2)r^2\cdot(\pi)/(5)$

which is equivalen to

$89=(1)/(10)\pi r^2$

Then, by multiplying both sides by 10, we have

$890=\pi\cdot r^2$

and by dividing both sides by Pi, we get

$\begin{gathered} (890)/(\pi)=r^2 \\ \text{or equivalently,} \\ (890)/(3.1416)=r^2 \end{gathered}$

which gives

$\begin{gathered} 283.2951=r^2 \\ or\text{ equivalently,} \\ r^2=283.2951 \end{gathered}$

Finally, by taking square root to both sides, we have

$r=\sqrt[]{283.2951}$

so, the radius is

$r=16.83\text{ meters}$

Therefore, the answer is option C

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