This week in advanced math we learned about Law of Cosines and Law of Sines. Law of Cosines was more difficult than Law of sines. I understand both of them.

Law of Cosine’s formula is:
(Opp. Leg)^2 = (adj. Leg) ^2 + (adj. leg) ^2 -2 ( adj. leg) x (adj. leg) x cos( angle between )

Example :
Suppose triangle ABC had 2 sides measuring c = 2cm and b = 4cm. The angle between them had a measure of A = 100 degrees. Find the third side.

First, you draw your triangle.

Second, you check to see if you can use law of sines. When you see that you can not, your last option is Law of cosine. Then, you plug into the formula.

a^2 = (2)^2 + (4)^2 – 2 (2) x (4) x cos(100 degrees)

Then, plug the entire equation into your calculator to get your answer.
a = square root((2)^2 + (4)^2 – 2 (2) x (4) x cos(100 degrees))

a = 4.773 cm