1. **Stating the problem:** We have a right triangle KLM with a right angle at L. The sides KL and LM are given as 47 and 94 respectively, and we need to find the angle $x^\circ$ at vertex M. 2. **Formula and rules:** In a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side. Here, angle $x$ is at M, so: $$\tan(x) = \frac{\text{opposite side}}{\text{adjacent side}}$$ 3. **Identify sides relative to angle $x$:** - Opposite side to angle $x$ is KL = 47 - Adjacent side to angle $x$ is LM = 94 4. **Calculate tangent:** $$\tan(x) = \frac{47}{94} = 0.5$$ 5. **Find angle $x$ using arctangent:** $$x = \tan^{-1}(0.5)$$ 6. **Evaluate angle:** Using a calculator or inverse tangent function, $$x \approx 26.57^\circ$$ **Final answer:** $$x \approx 26.57^\circ$$