Question

The image depicts a baseball field in the shape of a diamond, with specific focus on the relationship between home plate, first base, and second base. Home plate and first base are connected by a line segment measuring 90 feet. This forms a right triangle with the diagonal line from home plate to second base acting as the hypotenuse. The setup visually represents how one might calculate the distance from home plate to second base using the Pythagorean theorem.

The image shows a baseball field, where the distance from home plate to first base is 90 feet. What is the distance from home plate to second base to the nearest foot?

A. 180 feet
B. 64 feet
C. 127 feet
D. 156 feet

Answer 1

To find the distance from home plate to second base using the Pythagorean theorem, we can visualize the baseball diamond as a right triangle.

Given:
- The distance from home plate (H) to first base (1B) is 90 feet.
- The distance from first base (1B) to second base (2B) is also 90 feet because the bases are equidistant in a square layout.

To find the distance from home plate to second base (H to 2B), we can apply the Pythagorean theorem:

\[
c^2 = a^2 + b^2
\]

Where:
- \(c\) is the distance from home plate to second base.
- \(a\) is the distance from home plate to first base (90 feet).
- \(b\) is the distance from first base to second base (90 feet).

Substituting the values into the equation:

\[
c^2 = 90^2 + 90^2
\]

Calculating \(90^2\):

\[
c^2 = 8100 + 8100
\]
\[
c^2 = 16200
\]

Now taking the square root:

\[
c = \sqrt{16200}
\]

Calculating \(\sqrt{16200}\):

\[
c \approx 127.3 \text{ feet}
\]

Rounding to the nearest foot:

\[
c \approx 127 \text{ feet}
\]

Thus, the distance from home plate to second base is approximately **127 feet**.

Therefore, the correct answer is **C. 127 feet**.