Law of Cosines: Do I have to learn all three?

[anonmeans]

My book shows three rules for the Law of Cosines:

a² = b² + c² - 2bc cos A
b² = a² + c² - 2ac cos B
c² = a² + b² - 2ab cos C

Don't these all really mean the same thing? "To find (the square of) the length opposite an angle, square the other two sides, and subtract two times the two lengths times the cosine of that angle."

Thank you.

[stapel_eliz]

Don't these all really mean the same thing? "To find (the square of) the length opposite an angle, square the other two sides, and subtract two times the two lengths times the cosine of that angle."

Yes, all three forms do mean the exact same thing, and you've stated the meaning correctly. And, by understanding that meaning, you won't have to depend on a graphic being labelled with the "right" letters, because you'll be able to extract the necessary relationship yourself.

Good job!

Eliz.

[anonmeans]

Thanks. That's a lot easier.

[A CURSED BEAR]

Ya they all mean the same thing, you just need to know what you are solving for and rearrange accordingly.