This might be fundamental, but I can't explain this...

Having a triangle with side a=4, b=8 and A=30 degrees.

Using the Law of Sines, you can determine that this is a 30,60, 90 triangle.

Why is it that there is only one triangle possible? I was explained that when you use the law of sines to solve for a missing angle, you need to then check to see if there are other triangles possible by doing the following. (using the above example)

B = 90 degrees. 180 - 90 = 90. 90 + 30 (the measurement of A) = 120. 120 < 180 and therefore, normally, there would be 2 triangles possible.

However, my textbook says that there is only one triangle possible. Our teacher told us "That's the way it is with 90's" - which tells me nothing. Either I've done something wrong, or there's a principle I don't understand. Can someone explain?

Thank you!!