Law of Sines Not Working Right for You?

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. We, as humans, know that there are

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!

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9 Responses to Law of Sines Not Working Right for You?

    • Thanks for the kind words, Beni!

      I can probably explain it in one video because I’ve done it like your teacher has for 20+ years. After you do it poorly enough times, you start wondering why students aren’t understanding. So you start watching students and asking questions – both of the students and yourself.

      After a while, you see what craziness is going on in the problem and are able to figure out not just how to do it, but how to explain it.

      I know your question was rhetorical, but I think this is a real reason.

      Thanks for stopping in!

  1. What if the problem you are doing doesn’t say that the triangle is necessarily obtuse? How are you supposed to know whether you have one?

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