1. **State the problem:** We have a right triangle with hypotenuse 14, one leg 6, and the other leg $x$ unknown. We need to find the correct formula to calculate $x$. 2. **Recall the Pythagorean theorem:** For a right triangle with legs $a$ and $b$, and hypotenuse $c$, the relationship is $$c^2 = a^2 + b^2$$ 3. **Identify the sides:** Here, $c = 14$ (hypotenuse), one leg $a = 6$, and the other leg $b = x$. 4. **Apply the formula:** Substitute known values: $$14^2 = 6^2 + x^2$$ 5. **Solve for $x^2$:** $$x^2 = 14^2 - 6^2$$ 6. **Calculate the squares:** $$x^2 = 196 - 36 = 160$$ 7. **Find $x$ by taking the square root:** $$x = \sqrt{160} = 4\sqrt{10}$$ 8. **Conclusion:** The correct formula is $$x = \sqrt{14^2 - 6^2}$$ which matches the first option. **Final answer:** $x = \sqrt{14^2 - 6^2}$