To find the distance from home plate to second base on a baseball field, we can use the properties of a right triangle.
In a baseball diamond, the bases form a square, with each side (base) being 90 feet. When we consider the triangle formed by home plate, first base, and second base, we can see that:
- The distance from home plate to first base (one side of the square) is 90 feet.
- The distance from first base to second base (another side of the square) is also 90 feet.
To find the distance from home plate to second base (the hypotenuse of the right triangle formed), we can use the Pythagorean theorem:
\[ c = \sqrt{a^2 + b^2} \]
where:
- \( c \) is the hypotenuse (the distance from home plate to second base),
- \( a \) and \( b \) are the lengths of the other two sides (both 90 feet).
Plugging in the values:
\[ c = \sqrt{90^2 + 90^2} \] \[ c = \sqrt{8100 + 8100} \] \[ c = \sqrt{16200} \] \[ c \approx 127.28 \text{ feet} \]
Rounding to the nearest foot, the distance from home plate to second base is approximately 127 feet.
So the answer is 127 feet.