Law of sines

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Law sines means: Every percentage point contributes the same amount

Law of cosines: track the interactions. A interacts with B, B with A. Subtract the overlap from each.

Law of cosines is about keeping track of overlaps.

http://www.quora.com/Trigonometry-mathematics/What-is-an-intuitive-explanation-of-the-law-of-cosines

Analogy: Tracking the impact of components in a path.
Diagram:
Example: The actions could help, hurt, or have no impact.
Plain English: Track the impact of the parts on the whole. (Positive impact, Negative impact, zero impact)
Technical: Measure the impact directly. The Pythagorean Theorem works by tracking these “self-interactions”.