Question

A baseball field is being designed. There is 60 ft between the pitcher and 3rd baseman and 90 ft between the catcher and 3rd baseman. The half-way distance from the catcher to the 3rd baseman is 45 ft. How far is the distance between the pitcher and the catcher?

Answer 1

Using the Pythagorean theorem, the distance between the pitcher and the catcher is calculated to be approximately 108.17 feet.

Step-by-step explanation:

To solve for the distance between the pitcher and the catcher in the design of a baseball field, we can use the Pythagorean theorem as the distances form a right-angled triangle.

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 lengths of the other two sides. This can be written as c^2 = a^2 + b^2.

In our scenario, let's denote:

Distance between pitcher and 3rd baseman: a = 60 ft

Distance between catcher and 3rd baseman: b = 90 ft

Distance between pitcher and catcher: c (the hypotenuse in our right-angled triangle)

Using the Pythagorean theorem, we can solve for c:

c^2 = 60^2 + 90^2

c^2 = 3600 + 8100

c^2 = 11700

c = sqrt(11700) ≈ 108.17 ft

Thus, the distance between the pitcher and the catcher is approximately 108.17 feet.

Answer 2

30 ft

Step-by-step explanation:

Here, we want to calculate the distance between the pitcher and the catcher

Pitcher and 3rd baseman is 60 ft

Half-way distance between catcher and 3rd baseman is 45 ft; this means the full distance between both will be 2 * 45 = 90 ft

So the distance between pitcher and catcher will be 90 ft - 60 ft = 30 ft