Question

What is the law of cosines?

Answer 1

Cosider the triangle:

(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)`
`b^2=a^2+c^2-2ac*cos(beta)`
`c^2=a^2+b^2-2ab*cos(gamma)`

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 cm`
`c=10 cm`
`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`