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**.
Pythagorean Distance 438Ece
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.