1. The problem is to calculate $dA$ given by the formula $$dA = dB \frac{\sin 55^\circ}{\sin 60^\circ}$$ where $dB = 126.5$. 2. We use the sine values: $\sin 55^\circ \approx 0.8192$ and $\sin 60^\circ = 0.8660$. 3. Substitute these values into the formula: $$dA = 126.5 \times \frac{0.8192}{0.8660}$$ 4. Simplify the fraction: $$\frac{0.8192}{0.8660} \approx 0.9459$$ 5. Multiply: $$dA = 126.5 \times 0.9459 = 119.7$$ 6. The intermediate step you gave, $126.5 \times 1.057$, is incorrect because $\frac{\sin 55^\circ}{\sin 60^\circ} \neq 1.057$. The correct ratio is approximately $0.9459$. **Final answer:** $$dA \approx 119.7$$