A man goes 9 m due east and then 40 m due north. How far is he from the starting point?

Options

A. 35 m
B. 39 m
C. 41 m
D. 45 m

Answer

To solve the problem step by step, we will use the Pythagorean theorem, which is applicable in this scenario since the man’s movements create a right triangle.

### Step-by-Step Solution:

1. **Identify the Movements**:
- The man first moves 9 meters due east.
- Then he moves 40 meters due north.

2. **Visualize the Triangle**:
- Mark the starting point as point A.
- After moving east, mark the new position as point B (9 meters east of A).
- After moving north from point B, mark the final position as point C (40 meters north of B).

3. **Draw the Right Triangle**:
- The triangle formed is a right triangle with:
- AB = 9 meters (base)
- BC = 40 meters (perpendicular)
- AC = distance from the starting point A to the final position C (hypotenuse).

4. **Apply the Pythagorean Theorem**:
- According to the Pythagorean theorem:
\[ AC^2 = AB^2 + BC^2 \]
- Substitute the known values:
\[ AC^2 = (9)^2 + (40)^2 \]

5. **Calculate the Squares**:
- Calculate \(9^2\):
\[ 9^2 = 81 \]
- Calculate \(40^2\):
\[ 40^2 = 1600 \]

6. **Add the Squares**:
- Now add the squares:
\[ AC^2 = 81 + 1600 = 1681 \]

7. **Find AC**:
- To find AC, take the square root of both sides:
\[ AC = \sqrt{1681} \]
- Calculate the square root:
\[ AC = 41 \text{ meters} \]

8. **Conclusion**:
- The distance from the starting point to the final position is 41 meters.