1. **State the problem:** We have a right triangle with angles 30°, 60°, and 90°. The side opposite the 30° angle is given as $14\sqrt{3}$ km, and we need to find the hypotenuse $q$ in simplest radical form. 2. **Recall the properties of a 30°-60°-90° triangle:** - The side opposite 30° is half the hypotenuse. - The side opposite 60° is $\sqrt{3}$ times the side opposite 30°. 3. **Set up the relationship:** Let the hypotenuse be $q$. Then the side opposite 30° is $\frac{q}{2}$. 4. **Use the given side length:** $$\frac{q}{2} = 14\sqrt{3}$$ 5. **Solve for $q$:** Multiply both sides by 2: $$\cancel{\frac{q}{2}} \times 2 = 14\sqrt{3} \times 2$$ $$q = 28\sqrt{3}$$ 6. **Final answer:** The hypotenuse $q$ is $\boxed{28\sqrt{3}}$ kilometers.