A man goes 15 m due east and then 20 m due north .find his distance from the starting point .

Options

A. 35 m
B. 5 m
C. 25 m
D. 15 m

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Directions
The man starts at a point (let's call it point O). He first moves 15 meters due east and then 20 meters due north. We need to visualize this movement on a coordinate plane.

### Step 2: Visualize the Movement
- From point O, moving 15 meters east takes him to point A.
- From point A, moving 20 meters north takes him to point B.

### Step 3: Identify the Triangle
The movements create a right triangle:
- OA (the eastward movement) = 15 m
- AB (the northward movement) = 20 m
- OB (the distance from the starting point to the final point) is the hypotenuse of the triangle.

### Step 4: Apply the Pythagorean Theorem
According to the Pythagorean theorem:
\[ OB^2 = OA^2 + AB^2 \]
Substituting the known values:
\[ OB^2 = 15^2 + 20^2 \]

### Step 5: Calculate the Squares
Calculate \( 15^2 \) and \( 20^2 \):
- \( 15^2 = 225 \)
- \( 20^2 = 400 \)

### Step 6: Sum the Squares
Now, add these two results:
\[ OB^2 = 225 + 400 = 625 \]

### Step 7: Find the Length of OB
To find OB, take the square root of 625:
\[ OB = \sqrt{625} = 25 \]

### Conclusion
The distance from the starting point O to the final point B is 25 meters.

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