The ambiguous case of the sine rule has so far not been put on a VCAA exam. However, with the ever-strengthening cohort, I bet you there will be a question on it this year, so it's very good that you're not ignoring it like a lot of the state is. Basically, when you're finding an angle using the sine rule, there can be two solutions. Consider the following diagram:
So just say that you are required to find angle ABC And you are given sides a and b, and angle CAB. If you just make up a couple of numbers for these values and punch them into the calculator, you will see that it gives you an acute angle. However, you can clearly see from the diagram that the desired angle is definitely obtuse. Basically, if you're only given one angle, there are two possible triangles that can be created and the faded lines show how this is possible. Perhaps a clever way to remember these sorts of problems is to call them 'swingers'. Working out the ambiguous case is almost the same as working it out normally - once you receive your acute angle answer on the calculator, subtract it from 180. This will give you the correct answer.
Just remember, there are always two solutions for every sine rule question involving a missing angle, so be alert, especially because your calculator will only tell you one.
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