1. **State the problem:** We have a right triangle LMN with a right angle at M. 2. **Identify the sides:** The sides are LM = 12, MN = 9, and LN = 15. 3. **Understand the angle:** We want to find the side adjacent to angle \(\angle MLN\). 4. **Recall definitions:** In a triangle, the side adjacent to an angle is the side that forms the angle along with the vertex, excluding the side opposite the angle. 5. **Analyze angle \(\angle MLN\):** This angle is at vertex L, formed by points M and N. 6. **Sides forming \(\angle MLN\):** These are LM and LN. 7. **Opposite side:** The side opposite \(\angle MLN\) is MN. 8. **Conclusion:** The side adjacent to \(\angle MLN\) is LM. **Final answer:** LM is adjacent to \(\angle MLN\).