1. **State the problem:** We have a right triangle with an angle of 43° at vertex A, the vertical leg is 7 cm, the horizontal leg is $x$, and the hypotenuse is $h$. We want to find the length of $x$. 2. **Identify the trigonometric relationship:** Since we know the angle and the side opposite to it (7 cm), and we want to find the adjacent side $x$, we use the tangent function: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Apply the formula:** $$\tan(43^\circ) = \frac{7}{x}$$ 4. **Solve for $x$:** $$x = \frac{7}{\tan(43^\circ)}$$ 5. **Calculate the value:** Using a calculator, $\tan(43^\circ) \approx 0.9325$. $$x = \frac{7}{0.9325} \approx 7.5$$ 6. **Final answer:** The length of side $x$ is approximately **7.5 cm**.