**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 Cosinesis actually a different way of expressing the lengths of the sides of the triangle above.For example, the length of side

can be found by using the Pythagorean Theorem as followsa

Notice in the triangle above that we can substitute

forb cos Aandxforb sin A.yTherefore,

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.