Law of Cosines
This applet can help you visualize the aspects of one proof to the law of cosines. Check out section 5.7 of this Mathematics Vision Project module: http://www.mathematicsvisionproject.org/uploads/1/1/6/3/11636986/sec3_mod5_modgeo_se_041114.pdf
This applet has a checkbox, "Rectangles," that automatically colors the equal triangles. If you check the "Areas" checkbox, a textbox will appear over each rectangle showing its calculated area. Use the move tool and drag one of the squares to change the dimensions of the triangle and see if the areas of the rectangle still stay the same.
Lastly, the "c1" and "a1" checkboxes are there to help you isolate the right triangles that are used to find the sidelengths of the top two rectangles. try using the fact that the cosine of an angle is equal to the adjacent leg's length divided by the hypotenuse's length.