a baseball diamond is a square 27 cm on a side. how far is the homeplate from the second base?
pretty small diamond. the distance is juist the diagonal: 27√2 = 38 cm
To find the distance between home plate and second base on a baseball diamond, we can use the Pythagorean theorem.
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 other two sides.
In this case, the distance between home plate and second base forms the hypotenuse of a right-angled triangle.
Let's label the sides of the triangle as follows:
- The length from home plate to second base (the hypotenuse) as c.
- The length of one side of the square (the base of the triangle) as a.
We know that the baseball diamond is a square with each side measuring 27 cm. So, side a = 27 cm.
Now, we need to find the length of side c, which is the distance between home plate and second base.
Using the Pythagorean theorem, we can calculate c:
c^2 = a^2 + a^2
c^2 = 27^2 + 27^2
c^2 = 729 + 729
c^2 = 1458
Taking the square root of both sides:
c = √1458
Calculating the square root of 1458 gives us approximately 38.17 cm.
Therefore, the distance between home plate and second base on a baseball diamond is approximately 38.17 cm.