In high school baseball, the distance between the bases is 90 feet. In little league, the distance between the bases is 60 feet. The expression  b2+b2⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√  represents the distance between home plate and second base, where b represents the distance between bases.
 
M80200_000_006A.png
 
How much closer is second base to home plate in Little league than it is in high school baseball? Round your answer to the nearest hundredth.


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!

In high school baseball, the distance between the bases is 90 feet. In little league, the distance between the bases is 60 feet. The expression √(b²+b²) represents the distance between home plate and second base, where b represents the distance between bases. How much closer is second base to home plate in Little League than it is in high school baseball? Round your answer to the nearest hundredth.

Learn how to calculate the distance between home plate and second base in high school and Little League baseball using the Pythagorean theorem. This problem illustrates key geometric concepts such as the square root and distance formula, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation