How do I find the length of b, which is the side opposite B.
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Question

How do I find the length of b, which is the side opposite B. 
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jdoe0001 · Answer

"opposite side" is the side FACING OFF the angle
so if you put your EYE in the angle, you'll notice the "opposite side" in front of you

jdoe0001 · Answer

http://fouss.pbworks.com/f/tigratios.JPG so we could say that $\bf sin(B) = \cfrac{opposite}{hypotenuse}\implies hypotenuse\times sin(B) = opposite$