1. **State the problem:** Find the length of side $x$ in a right triangle where the hypotenuse is 13 cm and the angle adjacent to $x$ is 54° using the cosine ratio. 2. **Formula and explanation:** The cosine ratio in a right triangle is defined as: $$\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$$ where $\theta$ is the given angle. 3. **Apply the formula:** Here, $\theta = 54^\circ$, hypotenuse = 13 cm, and adjacent side = $x$. So, $$\cos(54^\circ) = \frac{x}{13}$$ 4. **Solve for $x$:** Multiply both sides by 13: $$x = 13 \times \cos(54^\circ)$$ 5. **Calculate the cosine value:** Using a calculator, $$\cos(54^\circ) \approx 0.5878$$ 6. **Find $x$:** $$x = 13 \times 0.5878 = 7.6414$$ 7. **Round to the nearest tenth:** $$x \approx 7.6 \text{ cm}$$ **Final answer:** The length of side $x$ is approximately **7.6 cm**.