pre-calculus about the law of sin

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Mathematics
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Question description

So, why is it that if I do 16/sin(x)=27.9606/sin(40.9658) i get the answer x=22.034281934928 not giving me multiply triangles since 180-22.034281934928=157.965718065072 plus 40.9658 then you will over 180 making the number of triangles possible one, but when you do 27.9606/sin(x)=16/sin(22.034281934928) x=40.9658 so then the number of possible triangles would be two since 180-40.9658=139.0342 and plus 22.034281934928 it allows for a second triangle. Please help explain why this is, and if they are the same thing?

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(Top Tutor) Daniel C.
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