Law of Sines: [tex]\frac{sin(a)}{A} =\frac{sin(b)}{B}[/tex] ,
where a is the angle of opposite of side A and b is the angle opposite of side B
Extend law of sines to all three sides and angles of the triangle to get:
[tex]\frac{sin(a)}{A} =\frac{sin(b)}{B} =\frac{sin(c)}{C}[/tex],
where a is the angle of opposite of side A, b is the angle opposite of side B, and c is the angle opposite of side C
Law of Cosines: [tex]C^{2}=A^{2} +B^{2} -2ABcos(c)[/tex] OR [tex]C = \sqrt{A^{2} +B^{2} -2ABcos(c)}[/tex],
where C is the unknown side, A and B are the two known sides, and angle c is the angle opposite of the unknown side
(algebraic manipulation will get you from equation 1 to 2 by taking the square root of both sides)
what many people tend to get confused for the law of cosines is that they label sides of a triangle ABC regardless of whether or not the side value is unknown or known. If you do this, just make sure that the unknown side is always isolated, not whatever the value side C of the triangle you labeled is.
