POINT OF INTEREST 5 - THE LAW OF COSINES
Copyright by Ingrid Stewart, Ph.D. Please Send Questions and Comments to email@example.com.
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.
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.