Question: Solve for $a$.\n\n$c$\n\n$a$\n\n$b = 17$\n\n$B$\n\n$50^\circ$\n\n$64^\circ$\n\n$A$\n\n$a = ?$\n\nLaw of Sines: $\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$\n\nRound your answer to the nearest hundredth.
1. **State the problem:** We are given a triangle with angles $A = 64^\circ$, $B = 50^\circ$, and side $b = 17$ opposite angle $B$. We need to find side $a$ opposite angle $A$.\n\n2. **Find angle $C$:** Since the sum of angles in a triangle is $180^\circ$,\n$$C = 180^\circ - A - B = 180^\circ - 64^\circ - 50^\circ = 66^\circ.$$\n\n3. **Recall the Law of Sines:**\n$$\frac{\sin A}{a} = \frac{\sin B}{b}.$$\nWe want to solve for $a$, so rearrange: \n$$a = b \cdot \frac{\sin A}{\sin B}.$$\n\n4. **Substitute known values:**\n$$a = 17 \cdot \frac{\sin 64^\circ}{\sin 50^\circ}.$$\n\n5. **Calculate sines:**\n$$\sin 64^\circ \approx 0.8988, \quad \sin 50^\circ \approx 0.7660.$$\n\n6. **Calculate $a$:**\n$$a = 17 \cdot \frac{0.8988}{0.7660} = 17 \cdot 1.1737 = 19.953.$$\n\n7. **Round to nearest hundredth:**\n$$a \approx 19.95.$$\n\n**Final answer:** $a = 19.95$.