Answer:
\(A = 22.342\,in^{2}\)
Step-by-step explanation:
The radius of the circle is:
\(2\cdot r \cdot \cos 30^{\textdegree} = 8\,in\)
\(r = \frac{8\,in}{2\cdot \cos 30^{\textdegree}}\)
\(r \approx 4.619\,in\)
Finally, the area of the segment is:
\(A = \left(\frac{120^{\textdegree}}{360^{\textdegree}} \right)\cdot \pi \cdot (4.619\,in)^{2}\)
\(A = 22.342\,in^{2}\)
