A proof of the sine rule

Here's a nice use of circle theorems: ever wondered why the sine rule works?


Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.


3 comments on “A proof of the sine rule

  • Pat Ballew

    Colin, I always tried to teach this as “in any triangle, the ratio of a side to the sine of the opposite angle is twice the radius, and wrote “corrections” to every textbook author who wrote the law of sines with “Sin A / a” instead of with sides on top….alas, I have mellowed now.
    btw, your students may be interested in knowing that it seems the term “Law of sines” was first applied to the spherical law, then extended to the planar version.

    • Colin

      Oh, I didn’t know about the spherical version! That’s neat 🙂

  • Graciela Rhodes

    I like this proof. I have not thought of it before. Thank you.

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I teach in my home in Abbotsbury Road, Weymouth.

It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby.

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