Shannon mistakenly mixed up angles A and B. Notice the side 9 is opposite angle B and not angle A.
She should replace every copy of uppercase A with uppercase B. Also, she should replace lowercase 'a' with lowercase b
This is what her steps should look like
[tex]\frac{\sin B}{b} = \frac{\sin C}{c}\\\\\frac{\sin B}{9} = \frac{\sin 125^{\circ}}{12}\\\\B= \sin^{-1}\left(\frac{9*\sin 125^{\circ}}{12}\right) \approx 37.9^{\circ}\\\\[/tex]
Then we can find angle A like this
[tex]A+B+C = 180\\\\A = 180 - B - C\\\\A \approx 180 - 37.9 - 125\\\\A \approx 17.1^{\circ}\\\\[/tex]
Angle A is approximately 17.1 degrees.
