1. **State the problem:** We have a right triangle KLM with a right angle at L. Side KL = 47, side LM = 94, and we need to find the angle $x$ at vertex M. 2. **Identify the sides relative to angle $x$:** - Side opposite to angle $x$ is KL = 47. - Side adjacent to angle $x$ is LM = 94. 3. **Use the tangent function:** The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. $$\tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{47}{94}$$ 4. **Calculate the ratio:** $$\frac{47}{94} = 0.5$$ 5. **Find the angle $x$ using the inverse tangent (arctan):** $$x = \tan^{-1}(0.5)$$ 6. **Calculate $x$:** Using a calculator, $$x \approx 26.565^{\circ}$$ 7. **Round to the nearest tenth:** $$x \approx 26.6^{\circ}$$ **Final answer:** $$x = 26.6^{\circ}$$