Law of Cosine

Law of Cosine, like Law of Sine, is one of the many things we learn in Pre-Calculus during the Trigonometry unit. The formula for Law of Cosine is:
                                                             a^2=b^2=c^2-2bcCosA
If need be if you're not solving for side length 'a' or the measure of angle A, you can switch the letters around to suit your needs. If you're solving for side length 'b' or the measure of angle B then your formula will look like this: b^2=a^2+c^2-2acCosB. But if you're solving for the side length 'c' or measure of angle C then the formula reads: c^2=a+b^2-2abCosC.

Like I previously posted in Law of Sine, the lower case letters mean side length and the capital letters mean angle measures. To find out if you need to use Law of Cosine then you need to check out if your triangle has at least 2 side lengths and an angle or all three side lengths.

I'm going to first show you how to use Law of Cosine to solve for a side length.

Now I'm going so show you how to use Law of Cosine to solve for an angle measurement.

Thanks for reading my post about Law of Cosine. Also, if you get an error then it could be either due to your calculator not being in degree mode or because there's no solution.

Law of Sine

Law of Sine is one of the many things a student learns in Pre-Calculus, and some even learn it in Geometry. Law of sine is very simply put as:
                                                    a                b                  c
                                                _____    =   _____  =   _______
                                                 CosA         Cos B          CosC

The lower case letters mean the side lengths of a triangle. The capital letters are angle measurements. To know that you're using Law of Sine, your problem must first involve a triangle. It also has to have at least 1 side length and two angles or 1 angle and 2 side lengths. Let's take a look at Example 1 to see how you can use this formula to find a side length.

This is how you use Law of Sine to solve for a side length, but now I'm going to show you how to use it to solve for an angle measurements.

This is how you solve a problem using law of sine. Watch for the next post over law of cosine.