This applet will give you the steps to finding the resultant vector using the Parallelogram Law, which includes the Law of Sines, Cosines or using Components. It does not show you the mathematics involved, only the steps.

After you input the direction and magnitude for each vector, approximate the location of the resultant vector. (You may have to resize the graph.)
While following the steps, write down the math that is required for each step.
Pick two new vectors and do the math, then check to see if you get the same answer as the applet.