Really the only thing you need to worry about is when you're using the sine rule to find an angle.
If you read the question carefully and look carefully at the diagram, you'll know when the angle you're trying to find is obtuse.
If you use the sine rule to find the angle, then your calculator will give an answer which is less than 90 degrees. You know it needs to be greater than 90 degrees, so all you need to do is to take the calculator answer away from 180° and there's the obtuse angle.
There's no problem with using the cosine rule to find any angle. Your calculator will give you the obtuse angle.
That's all you'll need to worry about.
This is because the value of a sine ratio is positive in the 1st quadrant (acute) AND the 2nd quadrant (obtuse). On the other hand, the value of a cosine ratio is positive in the 1st quadrant (acute) but negative in the 2nd quadrant (obtuse).
Also, I know the diagrams are not to scale, but they're also not meant to deceive or trick you either. They're not going to throw in a diagram that clearly shows a very acute angle when it's supposed to be obtuse.
AND in all the past papers I've done, I've only seen this sort of problem pop up once, in an old catholic trial MIS paper.
