1. **State the problem:** Solve for $x$ in a right triangle where the hypotenuse is 13, one angle is 30°, and the right angle is 90°. 2. **Recall the trigonometric relationship:** In a right triangle, the cosine of an angle is the ratio of the adjacent side to the hypotenuse: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ 3. **Apply the formula:** Given $\theta = 30^\circ$, hypotenuse = 13, and adjacent side = $x$, we have: $$\cos(30^\circ) = \frac{x}{13}$$ 4. **Solve for $x$:** Multiply both sides by 13: $$x = 13 \times \cos(30^\circ)$$ 5. **Calculate $\cos(30^\circ)$:** $$\cos(30^\circ) = \frac{\sqrt{3}}{2} \approx 0.866$$ 6. **Find $x$ value:** $$x = 13 \times 0.866 = 11.258$$ **Final answer:** $$x \approx 11.26$$