To solve this problem, we need to calculate the distance between home plate and second base for both high school baseball and little league baseball.

Given:

• The distance between bases in high school baseball is $90$ feet.
• The distance between bases in little league baseball is $60$ feet.

The distance between home plate and second base forms the diagonal of a square with side length $b$. This can be calculated using the Pythagorean theorem:

$\text{Distance} = \sqrt{b^2 + b^2} = \sqrt{2b^2} = b \sqrt{2}$

Step 1: Calculate the Distance in High School Baseball

For high school baseball, where $b = 90$ feet:

$\text{Distance}_{\text{high school}} = 90 \sqrt{2}$

Now, calculate $90 \sqrt{2}$:

$90 \sqrt{2} \approx 90 \times 1.414 = 127.28 \text{ feet}$

Step 2: Calculate the Distance in Little League Baseball

For little league baseball, where $b = 60$ feet:

$\text{Distance}_{\text{little league}} = 60 \sqrt{2}$

Now, calculate $60 \sqrt{2}$:

$60 \sqrt{2} \approx 60 \times 1.414 = 84.85 \text{ feet}$

Step 3: Find the Difference in Distance

Now, we find the difference between the distances:

$\text{Difference} = \text{Distance}_{\text{high school}} - \text{Distance}_{\text{little league}} = 127.28 - 84.85$

Calculate the difference:

$\text{Difference} \approx 42.43 \text{ feet}$

Final Answer

The second base is approximately 42.43 feet closer to home plate in Little League than in high school baseball.

Would you like more details or have any questions?

Related Questions to Explore:

1. What is the diagonal distance between any two adjacent bases in a rectangular baseball field?
2. How would the distance change if the field was a rectangle instead of a square?
3. How do these calculations apply to softball fields where base distances differ?
4. What is the significance of the Pythagorean theorem in sports and real-world applications?
5. How would the result change if the base distances were given in meters instead of feet?

Tip:

Understanding the Pythagorean theorem is useful for problems involving diagonal distances in geometry!