Aman walked 63m due east. He then turned and walkeed for 16 m due north. How far is he from the starting point ?

Answer

To find out how far Aman is from his starting point after walking 63 meters east and then 16 meters north, we can use the Pythagorean theorem. Here’s a step-by-step solution:

### Step 1: Understand the Movement
Aman starts at point A and walks 63 meters east to point B. Then, he turns and walks 16 meters north to point C. We need to find the distance from point A to point C.

### Step 2: Draw the Diagram
Draw a right triangle where:
- Point A is the starting point.
- Point B is 63 meters east of A.
- Point C is 16 meters north of B.
This forms a right triangle with:
- AB = 63 meters (horizontal leg)
- BC = 16 meters (vertical leg)

### Step 3: Apply the Pythagorean Theorem
According to the Pythagorean theorem, in a right triangle:
\[ AC^2 = AB^2 + BC^2 \]
Where:
- AC is the hypotenuse (the distance from A to C),
- AB is one leg (63 meters),
- BC is the other leg (16 meters).

### Step 4: Substitute the Values
Substituting the values into the equation:
\[ AC^2 = 63^2 + 16^2 \]

### Step 5: Calculate the Squares
Now calculate \( 63^2 \) and \( 16^2 \):
- \( 63^2 = 3969 \)
- \( 16^2 = 256 \)

### Step 6: Add the Squares
Now add these two results:
\[ AC^2 = 3969 + 256 = 4225 \]

### Step 7: Take the Square Root
To find AC, take the square root of 4225:
\[ AC = \sqrt{4225} = 65 \]

### Final Answer
Aman is 65 meters away from the starting point.

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