A man goes 12 m due West and then 9m due North. How far is he from the starting point?

Options

A. 12 m
B. 15 m
C. 18 m
D. 24 m

Answer

To find out how far the man is from the starting point after moving 12 meters due West and then 9 meters due North, we can use the Pythagorean theorem. Let's break down the solution step by step.

### Step 1: Understand the Movement
The man starts at point A. He moves 12 meters to the West to reach point B, and then he moves 9 meters North to reach point C. We need to find the distance from point A to point C.

### Step 2: Visualize the Triangle
We can visualize this movement as a right triangle:
- The horizontal leg (AB) represents the distance moved West (12 m).
- The vertical leg (BC) represents the distance moved North (9 m).
- The hypotenuse (AC) represents the distance from the starting point to the final point.

### 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 point (which we want to find).
- \( AB = 12 \, m \) (the distance moved West).
- \( BC = 9 \, m \) (the distance moved North).

### Step 4: Substitute the Values
Now, substitute the known values into the equation:
\[ AC^2 = 12^2 + 9^2 \]

Calculating the squares:
\[ AC^2 = 144 + 81 \]

### Step 5: Add the Results
Now, add the results:
\[ AC^2 = 225 \]

### Step 6: Take the Square Root
To find \( AC \), take the square root of both sides:
\[ AC = \sqrt{225} \]

Calculating the square root:
\[ AC = 15 \]

### Conclusion
The distance from the starting point to the final point (point C) is 15 meters.

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