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when working with trig functions. is there a trick to knowing if there are 2 solutions while filling out a triangle without memorizing your sines and cosines. or do I need to be subtracting all numbers I get by 180 then sin/cos them to see if they have the same number? doing law of sines right now. I would like to make it intuitive somehow without chasing rabbits on every problem if there is a way. thanks I attempted to attach a pic of the problem.

using the law of sines I got C is 50 and B is 72. rounding to the tens place for simplicity. this is just independent study not for a class. but my issue is the answer has 2 answers. I understand why. but I am curious if there is a way to tell without plugging numbers in and trying.

thanks

using the law of sines I got C is 50 and B is 72. rounding to the tens place for simplicity. this is just independent study not for a class. but my issue is the answer has 2 answers. I understand why. but I am curious if there is a way to tell without plugging numbers in and trying.

thanks