What is the law of cosines?

1 Answer
Dec 21, 2014

Cosider the triangle:

enter image source here
(Picture source: Wikipedia)

you can relate the sides of this triangle in a kind of "extended" form of Pitagora's Theorem giving:

a^2=b^2+c^2-2bc*cos(alpha)a2=b2+c22bccos(α)
b^2=a^2+c^2-2ac*cos(beta)b2=a2+c22accos(β)
c^2=a^2+b^2-2ab*cos(gamma)c2=a2+b22abcos(γ)

As you can see you use this law when your triangle is not a right-angled one.

Example:
Consider the above triangle in which:
a=8 cma=8cm
c=10 cmc=10cm
beta=60° therefore:
b^2=a^2+c^2-2ac*cos(beta)
b^2=8^2+10^2-2*8*10*cos(60°) but cos(60°)=1/2
so: b^2=84 and b=sqrt(84)= 9,2 cm