1. **State the problem:** Calculate the value of $$\frac{\sin(73)}{\sin(76)} \times 9.6$$. 2. **Recall the formula:** We use the sine function values and multiply the fraction by 9.6. 3. **Calculate sine values:** $$\sin(73^\circ) \approx 0.9563$$ $$\sin(76^\circ) \approx 0.9703$$ 4. **Form the fraction:** $$\frac{\sin(73)}{\sin(76)} = \frac{0.9563}{0.9703}$$ 5. **Simplify the fraction:** $$= \frac{\cancel{0.9563}}{\cancel{0.9703}} \approx 0.9857$$ 6. **Multiply by 9.6:** $$0.9857 \times 9.6 = 9.463$$ 7. **Final answer:** $$\boxed{9.46}$$ (rounded to two decimal places)