Subjects geometry

Car Distance 198660

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** Two cars start from the same point. One travels north 4 km, the other east 3 km. We want to find the straight-line distance between them. 2. **Formula used:** We use the Pythagorean theorem for right triangles: $$c = \sqrt{a^2 + b^2}$$ where $a$ and $b$ are the legs, and $c$ is the hypotenuse (distance between cars). 3. **Identify values:** Here, $a = 4$ km (northbound), $b = 3$ km (eastbound). 4. **Calculate:** $$c = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25}$$ 5. **Simplify:** $$c = 5$$ 6. **Interpretation:** The cars are 5 kilometers apart in a straight line. This uses the Pythagorean theorem to find the hypotenuse of a right triangle formed by the cars' paths.