A man goes 150 m due east and then 200 m due north. How far is he from the starting point ?

Answer

To solve the problem of how far the man is from his starting point after moving 150 m due east and then 200 m due north, we can use the Pythagorean theorem. Here’s a step-by-step solution:

### Step 1: Understand the Movement
The man moves in two directions:
- First, he moves 150 m due east.
- Then, he moves 200 m due north.

### Step 2: Visualize the Path
We can visualize this movement as forming a right triangle:
- Let point A be the starting point.
- Point B is where he ends up after moving east (150 m).
- Point C is where he ends up after moving north from point B (200 m).

### Step 3: Identify the Sides of the Triangle
In triangle ABC:
- Side AB (the distance moved east) = 150 m
- Side BC (the distance moved north) = 200 m
- Side AC (the distance from the starting point to the final point) is what we need to find.

### Step 4: Apply the Pythagorean Theorem
According to the Pythagorean theorem:
\[ AC^2 = AB^2 + BC^2 \]

### Step 5: Substitute the Values
Substituting the known values into the equation:
\[ AC^2 = (150)^2 + (200)^2 \]

### Step 6: Calculate the Squares
Calculating the squares:
- \( (150)^2 = 22500 \)
- \( (200)^2 = 40000 \)

### Step 7: Add the Squares
Now add these two results:
\[ AC^2 = 22500 + 40000 = 62500 \]

### Step 8: Take the Square Root
To find AC, take the square root of 62500:
\[ AC = \sqrt{62500} = 250 \text{ m} \]

### Final Answer
The distance from the starting point is **250 m**.

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