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

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Directions
The man moves 40 meters due north and then 50 meters due west. We can visualize this movement on a coordinate plane where:
- North corresponds to the positive y-direction.
- West corresponds to the negative x-direction.

### Step 2: Define Points
Let:
- Point A be the starting point.
- Point B be the point after moving north.
- Point C be the final point after moving west.

### Step 3: Assign Coordinates
- Starting Point A (0, 0)
- After moving 40m north, Point B will be (0, 40).
- After moving 50m west from Point B, Point C will be (-50, 40).

### Step 4: Use the Pythagorean Theorem
To find the distance from the starting point A to the final point C, we can use the Pythagorean theorem. The distance AC can be calculated as:
\[ AC^2 = AB^2 + BC^2 \]

Where:
- \( AB = 40 \) meters (the distance north)
- \( BC = 50 \) meters (the distance west)

### Step 5: Substitute the Values
Substituting the values into the equation:
\[ AC^2 = 40^2 + 50^2 \]

### Step 6: Calculate the Squares
Calculating the squares:
\[ 40^2 = 1600 \]
\[ 50^2 = 2500 \]

### Step 7: Add the Squares
Now, add the two results:
\[ AC^2 = 1600 + 2500 = 4100 \]

### Step 8: Take the Square Root
To find AC, take the square root of 4100:
\[ AC = \sqrt{4100} \]

### Step 9: Calculate the Square Root
Calculating the square root:
\[ AC \approx 64.03 \text{ meters} \]

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

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