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# Sine rule yielding two angles watch

1. I understand that sometimes, the sine rule yields two angles, theta and 180 minus theta. However, I am unclear on the conditions in which this occurs. What criteria needs to be present for it to be the case that the sine rule will yield two angles, and how can I spot this in a question?
2. (Original post by Illidan2)
I understand that sometimes, the sine rule yields two angles, theta and 180 minus theta. However, I am unclear on the conditions in which this occurs. What criteria needs to be present for it to be the case that the sine rule will yield two angles, and how can I spot this in a question?
When you use the sine rule you will end up with

which generally has infinitely many solutions but since you're dealing with a triangle, only acute and obute angles will make sense. Your calculator will give you the acute angle and you can use (180 - acute angle) to get another solution i.e. the obtuse angle.

In summary, if the angle you're trying to find is acute then you use the calculator value and if it's obtuse then you do (180 - calculator value). If there is a different type of question that you're unsure about then please post it here.
3. (Original post by Illidan2)
I understand that sometimes, the sine rule yields two angles, theta and 180 minus theta. However, I am unclear on the conditions in which this occurs. What criteria needs to be present for it to be the case that the sine rule will yield two angles, and how can I spot this in a question?
To add to Notnek's answer, perhaps this example will make it even clearer.
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