What are the possible remaining angle measures in triangle ABC with A=40, AC=60, and BC=45?

a.

Question

What are the possible remaining angle measures in triangle ABC with A=40, AC=60, and BC=45?

a.<B=121<C=19 and B=59<c=18
b. <B=121 <C=19
c. <B=59 <C=81
d. No triangle can be formed with these measures.

anonymous · Answer

We can use the law of sines for this one. We have a side length and two angles. If we get back a sensible answer i.e. >0 and real valued then we should be good to go. The law of sines is
$$\frac{\sin(a)}{\alpha}=\frac{\sin(b)}{\beta}=\frac{\sin(c)}{\gamma} $$

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