Question

A baseball diamond is in the shape of a square. The distance from base to base is 90 feet how far does a catcher throw a ball from home plate to second base?

Answer 1

To find out how far a catcher throws the ball from home plate to second base on a baseball diamond, we use the Pythagorean theorem. The sides of the square base paths are 90 feet, which means the throw is the diagonal of the square. The calculation shows the catcher must throw the ball approximately 127.3 feet.

Step-by-step explanation:

The question asks how far a catcher must throw the ball from home plate to second base on a baseball diamond, which is a square with 90-foot sides. To find this distance, we use the Pythagorean theorem. The distance from home plate to second base is the diagonal of the square. Since the sides of the square are 90 feet, we have two sides of a right triangle, each measuring 90 feet. Applying the Pythagorean theorem (a² + b² = c²), where a and b are the sides and c is the diagonal, we get:

1. Calculate the square of the sides: 90² + 90²
2. This equals 8100 + 8100.
3. Add these together to get 16200.
4. Take the square root of 16200 to find c.
5. The square root of 16200 is 127.3 feet (approximately).

Therefore, the catcher must throw the ball approximately 127.3 feet to reach second base.