The Law of Sines -

The Law of Sines is used for solving triangles when you have one angle measure and two side lengths - one of which needs to be across from the known angle measure. It looks like so.
(Sin <A)/A = (Sin <B)/B = (Sin <C)/C
This basically means that the sine of any angle measure divided by the side length across from it will be the same as the same operations done with a different angle (and side length across from it) in the same triangle.

The Law of Cosines -

The Law of Cosines is very much like Pythagorean's theorem for non-right triangles. It is used to solve triangles when you know two sides and one angle, and the known angle measure is between the two sides. It looks like this (note that ^2 means squared). The variables can be changed at will.
A^2 = B^2 + C^2 + 2BC Cos <A

Triangle Properties

The sum of all the angles of a triangle is always 180 degrees. Also, the greatest angles are across from the longest sides, the next greatest across from the next longest, and the smallest across from the shortest.

Source: "Precalculus - a right trangle approach to trigonometry" - Sullivan, Sullivan. Published 2007 by Pearson Prentice Hall.

Definition of Trig - training problem

Law of Cosines - the Line of Sight

Law of Sines - When you gotta go

Law of Both - Observer's day off

The Means and Tricks