1. **State the problem:** We need to find the length of side BC in quadrilateral ABCD given angles and side lengths, using the sine and cosine rules. 2. **Given data:** - AB = 9.4 cm - AD = 12.8 cm - BD = 13.3 cm - \(\angle A = 72^\circ\) - \(\angle C = 54^\circ\) - \(\angle D = 39^\circ\) 3. **Use the sine rule in triangle BCD to find BC:** The sine rule states: $$\frac{q}{\sin(39^\circ)} = \frac{13.3}{\sin(54^\circ)}$$ where \(q = BC\). 4. **Rearrange to solve for \(q\):** $$q = \frac{13.3 \times \sin(39^\circ)}{\sin(54^\circ)}$$ 5. **Calculate the sines:** - \(\sin(39^\circ) \approx 0.6293\) - \(\sin(54^\circ) \approx 0.8090\) 6. **Substitute values:** $$q = \frac{13.3 \times 0.6293}{0.8090} \approx \frac{8.370}{0.8090} \approx 10.35$$ 7. **Final answer:** Length of BC is approximately \(10.4\) cm correct to 3 significant figures. **Summary:** Using the sine rule in triangle BCD, we found \(BC = 10.4\) cm.