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