if it is 90 feet between bases, how far is it from home to second base
It is 127.28 feet from home plate to second base.
equation?
The distance from home plate to second base can be calculated using the Pythagorean theorem, which states that a^2 + b^2 = c^2, where c is the hypotenuse (the distance between two points).
In this case, the distance between each base (90 feet) forms the two legs of a right triangle with the distance from home plate to second base as the hypotenuse. Therefore, the equation can be written as:
90^2 + 90^2 = c^2
8100 + 8100 = c^2
16200 = c^2
Taking the square root of both sides gives:
c = √16200
c ≈ 127.28
Therefore, the distance from home plate to second base is approximately 127.28 feet.
right triangle with sides a has hypotenuse a * sqrt 2
or
the diagonal of a square = side * sqrt 2
90 * sqrt 2 = 127.2792206
Yes, that is correct. Another way to calculate the distance from home plate to second base is to use the fact that in a right triangle, the length of the hypotenuse (c) is equal to the length of one of the sides (a) multiplied by the square root of 2 (c = a√2).
So in this case, the distance between bases (90 feet) is one of the sides of the right triangle, and the hypotenuse (the distance from home plate to second base) can be calculated as:
90 * √2 ≈ 127.2792206
Therefore, the distance from home plate to second base is approximately 127.2792206 feet, which is consistent with the previous calculation.
this is because
c^2 = a^2 + b^2 but b = a
so
c^2 = 2 a^2
c = a * sqrt 2
Yes, that is correct. In a right triangle where one of the angles is 45 degrees, the two legs are equal in length. This means that the Pythagorean theorem simplifies to c^2 = 2a^2. Taking the square root of both sides gives c = a√2, where c is the length of the hypotenuse and a is the length of one of the sides (legs) of the triangle.
In the context of the question, where the distance between bases is 90 feet, the length of the hypotenuse (distance from home plate to second base) can be calculated using c = 90√2 ≈ 127.2792206 feet.