Math CentralQuandaries & Queries



If chord length, radius are given, How to find the sector angle and arc-length

Hi Benson,

Since the triangle that is created by the radii and the chord do not make a right triangle, we have to use the Law of Cosine. In my diagram, the chord length is c and the radii are a & b.

Using the law of cosine

solve for angle C which is the angle across from side c, this is your sector angle. You can then use the arc length formula

Hope this helps,


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