Subjects geometry

Pythagorean Distance 438Ece

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1. **State the problem:** You drive 9 miles west, then 6 miles north. We need to find the straight-line distance from the start to the end point. 2. **Formula used:** This is a right triangle problem. Use the Pythagorean theorem: $$c = \sqrt{a^2 + b^2}$$ where $a$ and $b$ are the legs, and $c$ is the hypotenuse (straight-line distance). 3. **Identify values:** Here, $a = 9$ miles (west leg), $b = 6$ miles (north leg). 4. **Calculate:** $$c = \sqrt{9^2 + 6^2} = \sqrt{81 + 36} = \sqrt{117}$$ 5. **Simplify:** $$\sqrt{117} = \sqrt{9 \times 13} = \sqrt{9} \times \sqrt{13} = 3\sqrt{13}$$ 6. **Approximate:** $$3\sqrt{13} \approx 3 \times 3.605551275 = 10.816653825$$ 7. **Round to nearest tenth:** $$10.8$$ miles **Final answer:** The straight-line distance from the starting point is approximately **10.8 miles**.