Have you run into this? You get the “wrong answer” when you use a calculator and the Law of Sines to find an obtuse angle.
The problem isn’t that the Law of Sines doesn’t work (thanks @GMichaelGuy), but that you have to be cautious when dealing with the arcsine with an obtuse angle. Here’re the details:
I’ve concocted a triangle that’s pretty simple but has an obtuse angle. That’s the key here. The law of sines always “works” when you have all acute angles. It’s only when the angle in question is an obtuse angle that we have a problem. (and, as @GMichaelGuy pointed out, it always works, it just makes us do a little more work.)
Notice I used the arcsine. Turns out, the arcsine isn’t a function. Which means when you “undo” all the bits in the law of sines, technically you’ll get an infinite number of answers.
So it all boils down to the calculator not being able to determine if you want the obtuse angle when you solve for x using the law of sines!
What do you think? Any other questions on trig? Ask them in the comments.
And a big thanks to @mrlove314 for this question!