A man goes 40 m due north and then 50 m due west. Find his distance from the staring point.

Answer

To solve the problem step by step, we will use the Pythagorean theorem. The situation describes a right triangle formed by the man's movements.

### Step-by-Step Solution:

1. **Understanding the Movement:**
- The man moves 40 meters due north. Let's denote this movement as segment AB.
- Then he moves 50 meters due west. Let's denote this movement as segment BC.

2. **Identifying the Points:**
- Let point A be the starting point.
- Point B will be the position after moving 40 meters north.
- Point C will be the final position after moving 50 meters west.

3. **Drawing the Right Triangle:**
- The path from A to B (40 m north) and from B to C (50 m west) forms a right triangle ABC, where:
- AB = 40 m (vertical side)
- BC = 50 m (horizontal side)
- AC is the hypotenuse (the distance from the starting point A to the final point C).

4. **Applying the Pythagorean Theorem:**
- According to the Pythagorean theorem:
\[ AC^2 = AB^2 + BC^2 \]
- Substituting the values:
\[ AC^2 = (40)^2 + (50)^2 \]

5. **Calculating the Squares:**
- Calculate \(40^2\):
\[ 40^2 = 1600 \]
- Calculate \(50^2\):
\[ 50^2 = 2500 \]

6. **Adding the Squares:**
- Now, add the two results:
\[ AC^2 = 1600 + 2500 = 4100 \]

7. **Finding the Length of AC:**
- To find AC, take the square root of 4100:
\[ AC = \sqrt{4100} \]
- Calculating the square root:
\[ AC \approx 64.03 \text{ m} \]

### Final Answer:
The distance from the starting point to the final point is approximately **64.03 meters**.

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