1. **State the problem:** We need to find the angle $x$ in a right triangle where the hypotenuse is 5 and the adjacent side to angle $x$ is 3. 2. **Recall the trigonometric formula:** For a right triangle, the cosine of an angle is the ratio of the adjacent side to the hypotenuse: $$\cos(x) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ 3. **Apply the values:** $$\cos(x) = \frac{3}{5}$$ 4. **Calculate the angle $x$ using the inverse cosine function:** $$x = \cos^{-1}\left(\frac{3}{5}\right)$$ 5. **Evaluate the inverse cosine:** $$x = \cos^{-1}(0.6)$$ 6. **Use a calculator to find $x$ in degrees:** $$x \approx 53.1301^\circ$$ 7. **Round to the nearest tenth:** $$x \approx 53.1^\circ$$ **Final answer:** $x = 53.1^\circ$