How many triangles can be formed if in triangle abc, b=120, c=92 and c=42°?

I tried Law of Sines but remembered, that only determines even if you HAVE a triangle.

But still, you'll know if you have NO solution or at least a solution.

Here, by applying the Law of Sines...

sin(42°)/92 = sin(B)/120

92sin(B) = 80.295
sin(B)=0.873
B=60.78°

We know that this has at LEAST one solution now.

I've attached the formula instance when there's two triangles/solutions, or what we call the Ambiguous Case.

But I've also attached a picture of the one triangle case: two ways it could have one triangle for a solution.

Clearly, 92 is not bigger than 120 and since angle B is equal to 60.78 degrees, a does not equal h.

Well, now we know two triangles can be formed, and if you verify, yup.

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