1. **State the problem:** We need to find the angle $x^\circ$ in a right triangle where side $BC = 7.4$ units and side $CD = 5.6$ units, with a right angle at $C$. 2. **Identify the sides relative to angle $x$:** Since $BC$ is opposite angle $x$ and $CD$ is adjacent to angle $x$, we can use the tangent function which relates opposite and adjacent sides: $$\tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{BC}{CD} = \frac{7.4}{5.6}$$ 3. **Calculate the ratio:** $$\frac{7.4}{5.6} = 1.3214$$ 4. **Use the inverse tangent to find $x$:** $$x = \tan^{-1}(1.3214)$$ 5. **Calculate $x$ using a calculator:** $$x \approx 53.0^\circ$$ 6. **Final answer:** $$\boxed{x \approx 53.0^\circ}$$ This means the angle $x$ is approximately 53.0 degrees when rounded to the nearest tenth.