What is the formula for isolating b in the law of sines?

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The discussion focuses on isolating variable b in the law of sines formula, represented as sin α/a = sin β/b. One participant derives b as b = α sin β/sin α, while another suggests multiplying both sides by 1/sin β to arrive at b = sin α/(a sin β). This leads to the equation sin α/(a sin β) = 1/b, indicating a different approach to isolating b. The conversation highlights the variations in manipulating the law of sines to isolate specific variables. Ultimately, the formula for b can be expressed in multiple ways depending on the manipulation of the original equation.
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sin α/a = sin β/b

when my isolates b they get

b = α sin β/sinα

I would think to isolate b you would multiply both sides by 1/sinβ which would make

b = sin α/ a sin β
 
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Take sin α/a = sin β/b.

Multiply both sides by 1/sinβ and you get

sin α / (a sin β) = 1/b.
 

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