1. **State the problem:** We have a right triangle with angles 30°, 60°, and 90°, and the hypotenuse is given as $7\sqrt{3}$ meters. We need to find the length $j$ of the side opposite the 60° angle. 2. **Recall the properties of a 30°-60°-90° triangle:** In such a triangle, the sides are in the ratio $1 : \sqrt{3} : 2$, where: - The side opposite 30° is $x$, - The side opposite 60° is $x\sqrt{3}$, - The hypotenuse is $2x$. 3. **Set up the equation:** Given the hypotenuse is $7\sqrt{3}$, we have: $$2x = 7\sqrt{3}$$ 4. **Solve for $x$:** $$x = \frac{7\sqrt{3}}{2}$$ 5. **Find $j$, the side opposite 60°:** $$j = x\sqrt{3} = \frac{7\sqrt{3}}{2} \times \sqrt{3} = \frac{7 \times 3}{2} = \frac{21}{2}$$ 6. **Final answer:** $$j = \frac{21}{2}$$ meters. This is the simplest radical form and the exact length of side $j$.