Final answer:
The distance from home plate to third base in baseball, given that it's 90 feet from home to first base, is found using the Pythagorean theorem and is approximately 127.28 feet.
Step-by-step explanation:
In baseball, the layout of the bases forms a square, with each side measuring 90 feet, as it's also 90 feet from home to first base. To find the distance from home plate to third base, we can apply the Pythagorean theorem to this square because the distance from home plate to third base is the diagonal of the square. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²).
Let's define the sides of the baseball diamond as follows:
- Side a: From home plate to first base, 90 feet
- Side b: From first base to second base, which is also 90 feet
- Side c, the hypotenuse: From home plate to third base
Using the Pythagorean theorem:
a² + b² = c²
90² + 90² = c²
8100 + 8100 = c²
16200 = c²
c = √16200
c = 127.28 feet
So, the distance from home plate to third base is approximately 127.28 feet.