Law of sines and cosines in mathematics?

Answer 1

Consider a triangle with vertices A, B and C. Call the edge opposite a given vertex by the same letter, but lower case. So side a is opposite vertex A etc.

Law of Sines says:

SinA/a= SinB/b=SinC/c

If you prefer, you can split the equation into multiple separate ones:

SinA/a=SinB/b

Sin A/a=SinC/c etc.

(there is one more part of the law of Sines which most books leave out. If R is the radius of a circumcircle around triangle ABC, then SinA/a= SinB/b=SinC/c =2R and in case you forgot a circumcirlce of a triangle is a unique circle that passes through each of the triangle 3 vertices.)

The law of Cosines says:

a2 +b2 -2abCosC=c2

or a2 +b2 -2abCosB=b2

or a2 +b2 -2abCosA=a2