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Law of Sines (Illustrated)

The Law of Sines does tell us that for any triangle, the ratio of any side length to the sine of the angle opposite that side is equal to the ratio of any other side length to the sine of the angle opposite that other side. Yet it also tells us more.......click on the the "CHECK THIS OUT TOO !!!" link to see. Question: How can we prove that the value of any of these 3 "always-equal" ratios is the same as what's illustrated here?