1. **Problem 1:** Find the missing leg $b$ of a right triangle with hypotenuse 10 in and one leg 6 in. 2. Use the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse. 3. Substitute known values: $$6^2 + b^2 = 10^2$$ 4. Calculate squares: $$36 + b^2 = 100$$ 5. Isolate $b^2$: $$b^2 = 100 - 36 = 64$$ 6. Take the square root: $$b = \sqrt{64} = 8$$ inches. --- 7. **Problem 2:** Find the missing leg $a$ of a right triangle with hypotenuse 8 mi and one leg 7 mi. 8. Use the Pythagorean theorem: $$a^2 + 7^2 = 8^2$$ 9. Calculate squares: $$a^2 + 49 = 64$$ 10. Isolate $a^2$: $$a^2 = 64 - 49 = 15$$ 11. Take the square root and round to nearest tenth: $$a = \sqrt{15} \approx 3.9$$ miles. **Final answers:** - Missing leg $b = 8$ in - Missing leg $a \approx 3.9$ mi