1. **Stating the problem:** We have a right triangle with angles 30°, 60°, and 90°, and the side opposite the 30° angle is 10 km. We need to find the length of side $g$, which is opposite the 60° angle. 2. **Formula and important rules:** In a 30°-60°-90° triangle, the sides are in the ratio $1 : \sqrt{3} : 2$, where: - The side opposite 30° is the shortest side (let's call it $x$). - The side opposite 60° is $x\sqrt{3}$. - The hypotenuse (opposite 90°) is $2x$. 3. **Given:** The side opposite 30° is 10 km, so $x = 10$ km. 4. **Find $g$:** Since $g$ is opposite 60°, $$g = x\sqrt{3} = 10\sqrt{3}$$ 5. **Final answer:** $g = 10\sqrt{3}$ km. This corresponds to option c.