A man goes 24 m due east and then 10m due north.How far is he away from his initial position?

Options

A. 26 m
B. 25 m
C. 20 m
D. 15 m

Answer

To find out how far the man is from his initial position after moving 24 meters east and then 10 meters north, we can use the Pythagorean theorem. Here's how to solve the problem step by step:

### Step-by-Step Solution:

1. **Understand the Movement**:
- The man moves 24 meters to the east and then 10 meters to the north.
- This creates a right triangle where:
- One leg (base) is the distance moved east (24 m).
- The other leg (perpendicular) is the distance moved north (10 m).

2. **Identify the Triangle**:
- We can label the points:
- Let point O be the initial position (starting point).
- Point E is where he ends up after moving east (24 m).
- Point N is where he ends up after moving north from point E (10 m).
- The triangle formed is triangle OEN, where:
- OE = 24 m (base)
- EN = 10 m (perpendicular)
- ON = the hypotenuse (the distance we want to find).

3. **Apply the Pythagorean Theorem**:
- The Pythagorean theorem states that in a right triangle:
\[ ON^2 = OE^2 + EN^2 \]
- Substituting the values:
\[ ON^2 = 24^2 + 10^2 \]

4. **Calculate the Squares**:
- Calculate \(24^2\):
\[ 24^2 = 576 \]
- Calculate \(10^2\):
\[ 10^2 = 100 \]

5. **Sum the Squares**:
- Now add the squares:
\[ ON^2 = 576 + 100 = 676 \]

6. **Find the Length of the Hypotenuse**:
- To find ON, take the square root of 676:
\[ ON = \sqrt{676} = 26 \]

7. **Conclusion**:
- The man is 26 meters away from his initial position.

### Final Answer:
The man is 26 meters away from his initial position.