1. **State the problem:** We need to find the angle $x$ in a right triangle where the side adjacent to $x$ is 8.4 and the hypotenuse is 5. 2. **Identify the trigonometric function:** Since we have the adjacent side and the hypotenuse, we use the cosine function: $$\cos(x) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{8.4}{5}$$ 3. **Evaluate the fraction:** $$\frac{8.4}{5} = 1.68$$ 4. **Check the value:** The cosine of an angle cannot be greater than 1, so this indicates an error in the given side lengths or labeling. Typically, the hypotenuse is the longest side, but here 8.4 > 5. 5. **Re-examine the triangle:** If side 5 is adjacent and 8.4 is opposite, then use sine instead: $$\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{8.4}{5} = 1.68$$ Again, this is impossible. 6. **Assuming 8.4 is opposite and 5 is adjacent, use tangent:** $$\tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{8.4}{5}$$ 7. **Calculate tangent:** $$\tan(x) = 1.68$$ 8. **Find angle $x$ using arctangent:** $$x = \tan^{-1}(1.68)$$ 9. **Calculate $x$:** $$x \approx 59.0^\circ$$ **Final answer:** $$x \approx 59.0^\circ$$