$\frac{\sin 30^{\circ}}{14}=\frac{\sin 50^{\circ}}{b}$

Step 1 ：\(\frac{\sin 30^\circ}{14} = \frac{\sin 50^\circ}{b}\)

Step 2 ：\(b = \frac{14 \cdot \sin 50^\circ}{\sin 30^\circ}\)

Step 3 ：\(b \approx 21.45\)

Step 4 ：\(\boxed{b \approx 21.45}\)