Answer
See below
Work Step by Step
Use the law of sines:
$$\frac{b}{\sin B}=\frac{c}{\sin C}\\sin C=\frac{c\sin B}{b}\times b\\\sin C=\frac{32\sin 21^\circ}{17}\approx0.674\\C=42^\circ$$
The sum of the angles of the triangle is $180^\circ$
$$A+B+C=180^\circ\\A=180^\circ-B-C\\C=180^\circ-42^\circ=138^\circ\\A=21^\circ$$
There are two triangles. The first one has an angle of $C=42^\circ$, and the other one has an angle of $C=138^\circ$
