Question

The baseball diamond is really a square. The distance between each of the bases is 90 feet.

How far does the catcher have to throw the ball to get from home plate to second base? Round your answer to the nearest foot.

Answer 1

To get from home plate to second base, the catcher has to throw the ball across the diagonal of the square baseball diamond.

Using the Pythagorean theorem, we can find the length of the diagonal.

The diagonal is the hypotenuse of a right triangle, where the bases are the legs.

Let's call the length of each base x.

Using the Pythagorean theorem, the equation becomes:
x^2 + x^2 = diagonal^2
2x^2 = diagonal^2
Diagonal = sqrt(2x^2)

In this case, x is the distance between the bases, which is 90 feet.

So, Diagonal = sqrt(2 * 90^2) = sqrt(2 * 8100) = sqrt(16200) ≈ 127.28 feet.

Therefore, the catcher has to throw the ball approximately 127 feet to get from home plate to second base.