1. **State the problem:** We have a right triangle with two 45° angles, meaning it is an isosceles right triangle (45°-45°-90° triangle). The hypotenuse is given as $7\sqrt{3}$, and we need to find the length of the leg $x$. 2. **Recall the formula for a 45°-45°-90° triangle:** In such a triangle, the legs are equal, and the hypotenuse is $\sqrt{2}$ times the length of a leg. This means: $$\text{hypotenuse} = x \times \sqrt{2}$$ 3. **Set up the equation:** Given the hypotenuse is $7\sqrt{3}$, we have: $$7\sqrt{3} = x \sqrt{2}$$ 4. **Solve for $x$:** Divide both sides by $\sqrt{2}$: $$x = \frac{7\sqrt{3}}{\sqrt{2}}$$ 5. **Simplify the expression:** Rationalize the denominator by multiplying numerator and denominator by $\sqrt{2}$: $$x = \frac{7\sqrt{3} \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}} = \frac{7\sqrt{6}}{2}$$ 6. **Final answer:** The length of the leg $x$ is: $$x = \frac{7\sqrt{6}}{2}$$