on he teachers baseball team, they are measuring to put the bases down. ms.accardo wants it like a professiona; field. On a professional baseball field, the distance from one base to the next is 90 ft.what is the distance between home plate and second base? use the pythagorean theorem to find out it the distance is a perfect square. show all work
a^2 + b^2 = c^2
90^2 + 90^2 = c^2
8100 + 8100 = c^2
16,200 = c^2
127.279 = c
To find the distance between home plate and second base, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the path from home plate to second base can be treated as the hypotenuse of a right triangle, with the other two sides being the distances along the first and third baselines.
Since the distance from one base to the next is 90 ft, we can consider the first and third base paths to form two sides of a right-angled triangle. Let's call the distance along the first baseline "a" and the distance along the third baseline "b".
Using the Pythagorean theorem, we can calculate the hypotenuse (distance between home plate and second base).
a² + b² = c²
Since both "a" and "b" are equal to 90 ft, we have:
90² + 90² = c²
8100 + 8100 = c²
16200 = c²
To find out if the distance (c) is a perfect square, we need to take the square root of 16200:
c = √16200
Using a calculator, we find that c ≈ 127.279 ft.
Now, to check if c is a perfect square, we need to determine if it has an integer square root. Since 127.279 is not an integer, c is not a perfect square.
Therefore, the distance between home plate and second base is approximately 127.279 ft.