1. **State the problem:** Find the area of triangle RST given angle $S = 37^\circ$, side $ST = 15$ cm, and side $RT = 12.5$ cm. 2. **Formula used:** The area of a triangle when two sides and the included angle are known is given by: $$\text{Area} = \frac{1}{2}ab\sin(C)$$ where $a$ and $b$ are the sides enclosing angle $C$. 3. **Identify sides and angle:** Here, sides $ST$ and $RT$ enclose angle $S$, so $a = 15$, $b = 12.5$, and $C = 37^\circ$. 4. **Calculate the area:** $$\text{Area} = \frac{1}{2} \times 15 \times 12.5 \times \sin(37^\circ)$$ 5. **Evaluate $\sin(37^\circ)$:** $$\sin(37^\circ) \approx 0.6018$$ 6. **Substitute and multiply:** $$\text{Area} = \frac{1}{2} \times 15 \times 12.5 \times 0.6018 = 7.5 \times 12.5 \times 0.6018$$ 7. **Calculate intermediate multiplication:** $$7.5 \times 12.5 = 93.75$$ 8. **Final area calculation:** $$93.75 \times 0.6018 \approx 56.39$$ **Answer:** The area of triangle RST is approximately $56.39$ square centimeters.