Section 6.2 Law of cosines

Allright people, we probably have the most challenging lesson ever right here!

or not...

Its just the law of cosines, which we all learned in geometry. This law is used to relate the three sides of a triangle to one angle.








The law of cosines is: c² = b² + a² – 2ab*Cos(C)





You can use this equation to find any side or angle as long as you are given either two sides and an angle or three sides.

You can solve the equation to give you the missing angle too.

C = Cos^-1((c² -b² - a²)/-2ab)

Example 1. Given triangle XYZ, if y = 8, z = 6, and X = 172 Degrees. Find x.

x² = 8² + 6² – 2(8)(6)*Cos(172)
x² = 100- (-95.066)
x= Squareroot(195.o66)
x = 13.967

Example 2. Given triangle UMP, if u = 12, m = 22, and p = 16. Find M.

M = Cos^-1((22² -12² - 16^{2 )}/-2(12)(16))
M = Cos^-1(84/-384)
M = 102.636

And that is all you need to know about the law of cosines. For more information see http://hyperphysics.phy-astr.gsu.edu/Hbase/lcos.html

Leo, you are next man. Do me proud.