To find the area of a [tex]\(60^{\circ}\)[/tex] sector of a circle with an area of [tex]\(30 \, \text{in}^2\)[/tex], follow these steps:
1. Find the fraction of the circle that the [tex]\(60^{\circ}\)[/tex] sector represents:
A circle is divided into [tex]\(360^{\circ}\)[/tex]. So, the fraction of the circle that a [tex]\(60^{\circ}\)[/tex] sector represents is:
[tex]\[
\frac{60}{360}
\][/tex]
Simplify this fraction:
[tex]\[
\frac{60}{360} = \frac{1}{6}
\][/tex]
2. Calculate the area of the sector:
The area of a sector is given by the product of the fraction of the circle and the total area of the circle. In this case, multiply the fraction by the total area of the circle:
[tex]\[
\text{Area of sector} = \frac{1}{6} \times 30 \, \text{in}^2
\][/tex]
Simplify the multiplication:
[tex]\[
\text{Area of sector} = 5 \, \text{in}^2
\][/tex]
After going through these steps, the area of the [tex]\(60^{\circ}\)[/tex] sector of the circle is [tex]\(5 \, \text{in}^2\)[/tex].
Therefore, the answer is:
A. 5 in[tex]\(^2\)[/tex]
