



 
Hi Lindsay. Here's a method that solves this problem for any regular ngon inscribed in a circle of radius r. A regular ngon divides the circle into n pieces, so the central angle of the triangle I've drawn is a full circle divided by n: 360°/n. The Law of Cosines applies to any triangle and relates the three side lengths and a single angle, just as we have here. In general it says this:
In the case of our regular ngon, we have a = b = r and C = 360°/n, so we simplify it to:
which makes a final equation: If you wanted the perimeter of the ngon, you would just multiply this by n of course. For your question Lindsay, just put 5 units in for r and 8 in for n and you can calculate c. Hope this helps,  


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