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

Options

A. 34 m
B. 17 m
C. 26 m
D. 28 m

Answer

To find out how far the man is from his starting point after moving 24 meters due west and then 10 meters due north, we can use the Pythagorean theorem. Here’s a step-by-step solution:

### Step 1: Understand the movements
The man first moves 24 meters to the west and then 10 meters to the north. We can visualize this as a right triangle where:
- One leg (base) is the distance moved west (24 m).
- The other leg (perpendicular) is the distance moved north (10 m).

### Step 2: Identify the right triangle
Let’s denote:
- Point A as the starting point.
- Point B as the point after moving west (24 m).
- Point C as the final position after moving north (10 m).

### Step 3: Apply the Pythagorean theorem
According to the Pythagorean theorem:
\[ AC^2 = AB^2 + BC^2 \]
Where:
- \( AC \) is the distance from the starting point to the final position.
- \( AB = 24 \) m (distance moved west).
- \( BC = 10 \) m (distance moved north).

### Step 4: Substitute the values
Now, substituting the values into the equation:
\[ AC^2 = 24^2 + 10^2 \]

### Step 5: Calculate the squares
Calculating the squares:
- \( 24^2 = 576 \)
- \( 10^2 = 100 \)

### Step 6: Add the squares
Now, add these values:
\[ AC^2 = 576 + 100 = 676 \]

### Step 7: Find the square root
To find \( AC \), take the square root of 676:
\[ AC = \sqrt{676} = 26 \]

### Conclusion
The man is 26 meters away from the starting point.

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