Question

Express answer in exact form.

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

The answer has to be left in like:(64/4) * pi - (9)*sqrt 3

Answer 1

\[\text{segment} \text{width}= \text{2*r} \text{ Sin}\left[\frac{\theta }{2}\right]\]\[8=2 r\text{ }\text{Sin}\left[\frac{120{}^{\circ}}{2}\right]\]\[r=\frac{8}{\sqrt{3}} \]\[\text{segment} \text{ area}= \frac{1}{2}r^2(\theta -\text{Sin}[\theta ])\]=\[\frac{32}{3} \left(120 {}^{\circ}-\frac{\sqrt{3}}{2}\right) \text{ or } \frac{32}{3} \left(\frac{2\pi }{3}-\frac{\sqrt{3}}{2}\right) \]= 13.1026