How do I determine how many possible triangles (solutions) based on this data? I'm confused as to how I can know how many solutions there are, can somebody help explain it to me? Thanks.

Question

anonymous · Answer

attachment

anonymous · Answer

Angles in a triangle add up to 180.

anonymous · Answer

Yes, but after using the law of sines to get SinA, I can assume that C=180-SinA-SinB--but that doesn't imply more than one solution

anonymous · Answer

Atleast not as I understand it

anonymous · Answer

Angle Side Side is not enough to judge triangle congruence.

anonymous · Answer

But you should draw it anyway.

anonymous · Answer

If law of sines gives you $A$, then you can find $C$.

ganeshie8 · Answer

you will get some expression like this :
sin(A) = k

find the solutions for A between (0, 180)

ganeshie8 · Answer

number  of different solutions gives you different triangles etc..

anonymous · Answer

Would this work?$$
\frac{\sin(B)}{b} = \frac{sin(A)}{a}
$$

anonymous · Answer

But isn't the range of sine -90 to 90?

anonymous · Answer

It would be 0 to 180

ganeshie8 · Answer

range of sin is [-1, 1]

ganeshie8 · Answer

domain is all angles, but you want only the angles between 0 and 180

anonymous · Answer

Okay yeah 0 to 180, that makes sense, so I want to figure out how many solutions there are between 0 and 180 for what exactly?

anonymous · Answer

SinA?

ganeshie8 · Answer

apply sin law, what do u get?

anonymous · Answer

Well, I get that SinA=.56431

anonymous · Answer

Is that what you're asking?

ganeshie8 · Answer

Yes, find the solutions of A between 0 and 180

anonymous · Answer

Well one is 34.35

anonymous · Answer

I'm not sure how o find the other

ganeshie8 · Answer

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