1. **State the problem:** We are given a right triangle with vertices L, N, and M, where angle N is the right angle. The sides are LN = 5, NM = 12, and hypotenuse LM = 13. We need to find $\sin(L)$ rounded to two decimal places. 2. **Recall the formula:** For any angle in a right triangle, $\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$. 3. **Identify the opposite side to angle L:** The side opposite angle L is NM, which is 12. 4. **Calculate $\sin(L)$:** $$\sin(L) = \frac{12}{13}$$ 5. **Evaluate the fraction:** $$\frac{12}{13} \approx 0.9230769$$ 6. **Round to two decimal places:** $$\sin(L) \approx 0.92$$ --- 7. **Second question:** Write $\sin 30^\circ$ as a fraction. 8. **Recall the special right triangle rule:** $\sin 30^\circ = \frac{1}{2}$. **Final answers:** - $\sin(L) \approx 0.92$ - $\sin 30^\circ = \frac{1}{2}$