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A segment of a circle has a 120 arc and a chord of 8in. Find the area of the segment.

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Bohotnesstherealoneidn
A segment of a circle has a 120 arc and a chord of 8in. The area of the segment = (120/360) x 3.14 x 8^2 = 67 in^2
Xero099idn

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]

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