1. **State the problem:** We are given a right triangle with angle $x$ at vertex $B$, the side opposite $x$ is 7.4 units, and the side adjacent to $x$ is 5.6 units. We need to find the value of angle $x$. 2. **Formula used:** To find an angle in a right triangle when opposite and adjacent sides are known, use the tangent function: $$\tan(x) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Apply the formula:** $$\tan(x) = \frac{7.4}{5.6}$$ 4. **Calculate the ratio:** $$\tan(x) = 1.3214$$ 5. **Find the angle $x$ by taking the arctangent (inverse tangent):** $$x = \tan^{-1}(1.3214)$$ 6. **Evaluate the arctangent:** $$x \approx 53.1^\circ$$ 7. **Conclusion:** The angle $x$ measures approximately $53.1^\circ$.