Richard starts from home and goes `80` m due North and then `39` m due West to reach his school. How far is his school from his home ?

Answer

To find the distance from Richard's home to his school, we can visualize the problem as a right triangle. Here's how we can solve it step by step:

### Step 1: Understand the movement
Richard first moves 80 meters due North and then 39 meters due West. This creates a right triangle where:
- The vertical side (North) is 80 meters (AB).
- The horizontal side (West) is 39 meters (BC).

### Step 2: Draw a diagram
Draw a right triangle:
- Label the starting point (home) as point A.
- Label the point after moving North as point B (80 m from A).
- Label the final point (school) as point C (39 m from B, moving West).

### Step 3: Apply the Pythagorean theorem
According to the Pythagorean theorem:
\[ AC^2 = AB^2 + BC^2 \]
Where:
- \( AC \) is the distance from home to school (the hypotenuse).
- \( AB = 80 \) m (the vertical side).
- \( BC = 39 \) m (the horizontal side).

### Step 4: Substitute the values
Now substitute the values into the equation:
\[ AC^2 = 80^2 + 39^2 \]

### Step 5: Calculate the squares
Calculate \( 80^2 \) and \( 39^2 \):
- \( 80^2 = 6400 \)
- \( 39^2 = 1521 \)

### Step 6: Add the squares
Now add the two results:
\[ AC^2 = 6400 + 1521 = 7921 \]

### Step 7: Take the square root
To find \( AC \), take the square root of 7921:
\[ AC = \sqrt{7921} = 89 \text{ m} \]

### Step 8: Conclusion
Thus, the distance from Richard's home to his school is 89 meters.

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