Final answer:
Using the Pythagorean theorem, the distance from home plate to second base, which is the diagonal of a square with 90-foot sides, is approximately 127 feet to the nearest foot.
Step-by-step explanation:
The distance from home plate to second base on a baseball infield, which is a square with each side measuring 90 feet, can be found using the Pythagorean theorem. We calculate the distance as the diagonal of the square, which is the hypotenuse of a right triangle whose legs are the sides of the square.
According to the Pythagorean theorem, the formula to calculate the hypotenuse (c) is:
c = √(a^2 + b^2)
Here, both sides a and b equal 90 feet. Substituting the values, we get:
c = √(90^2 + 90^2)
Which simplifies to:
c = √(8100 + 8100)
c = √(16200)
c ≈ 127 feet
To the nearest foot, it's approximately 127 feet from home plate to second base.