1. **State the problem:** We have a right triangle with angles 30°, 60°, and 90°. The side opposite the 60° angle is 4 miles, and we need to find the length of side $d$, which is opposite the 30° angle. 2. **Recall the special right triangle rules:** In a 30°-60°-90° triangle, the sides are in the ratio: $$1 : \sqrt{3} : 2$$ where 1 is the side opposite 30°, $\sqrt{3}$ is opposite 60°, and 2 is the hypotenuse. 3. **Identify the given side:** The side opposite 60° is given as 4 miles. According to the ratio, this side corresponds to $\sqrt{3}$ times the shortest side. 4. **Set up the equation:** Let the shortest side (opposite 30°) be $x$. Then: $$x \sqrt{3} = 4$$ 5. **Solve for $x$:** $$x = \frac{4}{\sqrt{3}}$$ 6. **Rationalize the denominator:** $$x = \frac{4}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{4\sqrt{3}}{3}$$ 7. **Conclusion:** The length $d$ opposite the 30° angle is: $$d = \frac{4\sqrt{3}}{3} \text{ miles}$$