1. **State the problem:** Solve for the side $x$ in a right triangle where one leg is 30, the right angle is between sides 30 and $x$, and the angles are 65° opposite side 30 and 59° adjacent to side $x$. 2. **Recall the triangle angle sum rule:** The sum of angles in a triangle is 180°. Here, the right angle is 90°, and the other two angles are 65° and 59°, which sum to 124°, so this is consistent. 3. **Use trigonometric ratios:** Since the right angle is between sides 30 and $x$, and the angle 65° is opposite side 30, side 30 is opposite 65°, and side $x$ is adjacent to 65°. 4. **Use the tangent function:** $$\tan(65^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{30}{x}$$ 5. **Solve for $x$:** $$x = \frac{30}{\tan(65^\circ)}$$ 6. **Calculate $\tan(65^\circ)$:** $$\tan(65^\circ) \approx 2.1445$$ 7. **Substitute and simplify:** $$x = \frac{30}{2.1445}$$ 8. **Intermediate step with cancellation:** $$x = \frac{30}{\cancel{2.1445}} \approx 13.985$$ 9. **Round to nearest tenth:** $$x \approx 14.0$$ **Final answer:** $x \approx 14.0$