POINT OF INTEREST 5 - THE LAW OF COSINES
Copyright by Ingrid Stewart, Ph.D.  Please Send Questions and Comments to ingrid.stewart@csn.edu.

Proof of the Law of Cosines

The Law of Cosines is actually a different way of expressing the lengths of the sides of the triangle above.

For example, the length of side a can be found by using the Pythagorean Theorem as follows

Notice in the triangle above that we can substitute b cos A for x and b sin A for y.

Therefore,

Finally, multiplying out and combining like terms results

A similar argument can be used for the other two sides and for a triangle having an obtuse angle.