A segment of a circle has a 120 arc and a chord of 8in. Find the area of the segment.
The arc is 120/360 = 1/3 around the circle. So the chord makes a triangle with 30-30-120 angles and sides radius, radius, 8 in.
Split this in the middle of the 120 angle to form two 30-60-90 triangles. The side lengths for the triangle are 4/sqrt(3), 4. The area is 8/sqrt(3), and since there are two the area is 16/sqrt(3) = 16sqrt(3)/3.
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