1. **State the problem:** We have a right triangle N-M-L with a right angle at M. Side N-M is 9.8, side N-L is 18, and we need to find the angle $x$ at vertex L. 2. **Identify the sides relative to angle $x$:** - Hypotenuse: $N-L = 18$ - Opposite side to angle $x$: $N-M = 9.8$ 3. **Use the sine function:** $$\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{9.8}{18}$$ 4. **Calculate the ratio:** $$\sin(x) = \frac{9.8}{18} \approx 0.5444$$ 5. **Find the angle $x$ by taking the inverse sine:** $$x = \sin^{-1}(0.5444)$$ 6. **Calculate $x$ using a calculator:** $$x \approx 33.0^\circ$$ 7. **Final answer:** $$\boxed{33.0^\circ}$$