1. **State the problem:** We have a triangle with angles 84°, 47°, and angle A, and sides opposite these angles labeled as a, 25, and b respectively. We know angle A is 49° and side opposite 47° is 25. We need to find the length of side b, which is opposite angle A. 2. **Recall the Law of Sines:** The Law of Sines states that in any triangle, $$\frac{a}{\sin 84^\circ} = \frac{25}{\sin 47^\circ} = \frac{b}{\sin 49^\circ}$$ 3. **Use the Law of Sines to find side b:** We can write $$b = \frac{25 \times \sin 49^\circ}{\sin 47^\circ}$$ 4. **Calculate the sine values:** $$\sin 49^\circ \approx 0.7547$$ $$\sin 47^\circ \approx 0.7314$$ 5. **Substitute and calculate b:** $$b = \frac{25 \times 0.7547}{0.7314}$$ 6. **Simplify the fraction:** $$b = 25 \times \frac{0.7547}{0.7314}$$ 7. **Calculate the division:** $$\frac{0.7547}{0.7314} \approx 1.0317$$ 8. **Calculate b:** $$b = 25 \times 1.0317 = 25.7925$$ 9. **Round to one decimal place:** $$b \approx 25.8$$ **Final answer:** The length of side b is approximately 25.8.