To find the distance from home plate to second base on a baseball field, we can use the geometry of the diamond shape formed by the bases. In a standard baseball field, the bases are arranged in a square, where each side of the square (the distance between adjacent bases) is 90 feet.
To find the distance from home plate to second base, we can treat this as the diagonal of the square formed by first base, second base, and third base. The distance to second base (the diagonal) can be calculated using the Pythagorean theorem.
Let \( a = 90 \) feet be the distance from home plate to first base (and also from first base to third base).
The distance \( d \) from home plate to second base can be expressed as:
\[ d = \sqrt{(a^2 + a^2)} = \sqrt{(90^2 + 90^2)} = \sqrt{(8100 + 8100)} = \sqrt{16200} \]
Calculating \( \sqrt{16200} \):
\[ \sqrt{16200} \approx 127.28 \]
Rounding to the nearest foot, the distance from home plate to second base is approximately:
\[ \boxed{127} \text{ feet.} \]