1. **State the problem:** We have a right triangle with vertices N, M, and L, right angle at M. Side NM = 1.1, side NL = 2.6, and we need to find angle $x^\circ$ at vertex L. 2. **Identify the sides relative to angle $x$:** - Hypotenuse: NL = 2.6 - Opposite side to angle $x$: NM = 1.1 3. **Formula used:** To find an angle in a right triangle, use the sine function: $$\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 4. **Apply the formula:** $$\sin(x) = \frac{1.1}{2.6}$$ 5. **Calculate the ratio:** $$\sin(x) = 0.4231$$ 6. **Find the angle $x$ by taking the inverse sine (arcsin):** $$x = \sin^{-1}(0.4231)$$ 7. **Calculate $x$ using a calculator:** $$x \approx 25.1^\circ$$ **Final answer:** $$x \approx 25.1^\circ$$