Cosine Law

It is only used if you have SAS or SSS.

Important:
~> Only use cosine law once, then use sine law to finish question.

If you are looking for side a, the following equation must be used:
a² = b² + c² -2bc cosA

If you are looking for side b, the following equation must be used:
b² = a² + c² -2ac cosB

If you are looking for side c, the following equation must be used:
c² = a² + b² -2ab cosC


Example:

You have a triangular-shaped garden that you want to fance. You know two sidesare 50 m and 80 m and the included angle (angle between the sides) is 100^o. How many meters of fencing do you need?











b² = a² + c² - 2ac cosB


b² = 80² + 50² - 2(80)(50) cos100


b² = 6400 + 2500 - (8000).34


b² = 6180


b = 78.61




Here's a sample problem looking for an angle using the cosine law:

Find C where a = 200 m, b = 155 m, c = 172 m.

c² = a² + b² - 2ab cosC
172² = 200² + 155² - 2(200)(155) cosC
29584 = 40000 + 24025 - 62000 cosC
29584 - 64025 = -62000 cosC
-34441 = -62000 cosC
------------------------
-62000
cosC = 0.56
C = 56.3

Mrs. Ingram also asked us to answer Exercise 25, numbers 1-7.

Next scribe.. Rochelm!! Bet you didn't see that coming! :D