Question

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

Answer 1

To find the distance from home plate to second base on a baseball field, we can treat the baseball diamond as a square, where each side (the distance from home plate to first base, first base to second base, etc.) is 90 feet.

To calculate the distance from home plate to second base, we can use the Pythagorean theorem. The distance from home plate to first base is one leg of the right triangle, and the distance from first base to second base is the other leg.

Here are the steps to find the distance:

1. Home plate to first base = 90 feet
2. First base to second base = 90 feet

Using the Pythagorean theorem:

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

where \( c \) is the distance from home plate to second base, \( a \) and \( b \) are the distances from home plate to first base and from first base to second base, respectively.

Substituting the values:

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

\[
c^2 = 8100 + 8100
\]

\[
c^2 = 16200
\]

Now, taking the square root:

\[
c = \sqrt{16200} \approx 127.28
\]

Rounding to the nearest foot gives us approximately 127 feet.

So the answer is:

**B. 127 feet**