The Importance of the Law of Cosines

Just a quick note on the more generic and far lest cited sibling of the Pythagorean theorem, the law of cosines. If you're like me, you were taught this formula sometime between the eighth and the eleventh grades and promptly forgot it after your exam. It's a formula that relates the length of one side of a triangle (any side), to its opposite angle and the lengths of the other two sides. The formula and its associated diagram, (courtesy of Wikipedia), are shown below:

If you keep it in mind, you'll start to see it show up all over the place, honest! For example it turned up in today's electromagnetism homework. We were tasked on determining the electrostatic potential at any point in a plane due to a ring of charge. Some of us put a significant amount of effort into determining a general formula for the distance from a point in the plane to any point on the circle. An industrious eight grader however, could have rattled the formula off by heart!

References:
http://en.wikipedia.org/wiki/Law_of_cosines

Picture of the Day:

From 1/25/13

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