A man goes 24m due wes and then 10 m due north. How far is he from the staring point?

Answer

To solve the problem step by step, we can visualize the man's movement and apply the Pythagorean theorem.

### Step-by-Step Solution:

1. **Understand the Movement**: The man moves 24 meters due west and then 10 meters due north. We can represent this movement on a coordinate plane. Let's assume the starting point is at the origin (0, 0).

2. **Determine the Coordinates**:
- After moving 24 meters west, the man's position will be (-24, 0).
- After moving 10 meters north, his new position will be (-24, 10).

3. **Visualize the Triangle**: The starting point (0, 0), the point after moving west (-24, 0), and the final point (-24, 10) form a right triangle. The horizontal leg of the triangle is 24 meters (west), and the vertical leg is 10 meters (north).

4. **Apply the Pythagorean Theorem**: According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
\[ c^2 = a^2 + b^2 \]
Here, \( a = 24 \) meters and \( b = 10 \) meters.
\[ c^2 = 24^2 + 10^2 \]

5. **Calculate the Squares**:
\[ 24^2 = 576 \]
\[ 10^2 = 100 \]
\[ c^2 = 576 + 100 = 676 \]

6. **Find the Length of the Hypotenuse**:
\[ c = \sqrt{676} = 26 \text{ meters} \]

7. **Conclusion**: The distance from the starting point is 26 meters.

### Final Answer:
The man is 26 meters away from the starting point.