1. **Problem statement:** We have a triangle with sides 14 and 10, and an angle of 15° opposite the unknown side $x$. We need to find $x$. 2. **Formula used:** We use the Law of Cosines, which states: $$x^2 = a^2 + b^2 - 2ab \cos(C)$$ where $a$ and $b$ are the known sides, and $C$ is the included angle. 3. **Identify values:** Here, $a=14$, $b=10$, and $C=15^\circ$. 4. **Calculate:** $$x^2 = 14^2 + 10^2 - 2 \times 14 \times 10 \times \cos(15^\circ)$$ $$x^2 = 196 + 100 - 280 \times \cos(15^\circ)$$ 5. **Evaluate cosine:** $$\cos(15^\circ) \approx 0.9659$$ 6. **Substitute:** $$x^2 = 296 - 280 \times 0.9659 = 296 - 270.452 = 25.548$$ 7. **Find $x$:** $$x = \sqrt{25.548} \approx 5.1$$ **Final answer:** $x \approx 5.1$ (to one decimal place).