To find the distance from home plate to second base on a baseball field, we can treat the baseball field as a square. The bases (home plate, first base, second base, and third base) form the corners of a square.
The distance from home plate to first base is given as 90 feet. Since the bases form a square, the distance from first base to second base is also 90 feet.
To find the distance from home plate to second base, we can use the Pythagorean theorem. The distance from home plate to second base is the hypotenuse of a right triangle where both legs are 90 feet (the distance from home plate to first base and from first base to second base).
Using the Pythagorean theorem:
\[ \text{Distance} = \sqrt{(90^2 + 90^2)} = \sqrt{(8100 + 8100)} = \sqrt{16200} = 90 \sqrt{2} \approx 127.28 \text{ feet} \]
Rounding to the nearest foot, the distance from home plate to second base is approximately 127 feet.