Question

1. a baseball diamond is really a square, and the distance between consecutive bases is 90 ft. how far does a catcher have to throw the ball to get it to second base if a runner tries to steal second?

Explanation:

Step1: Identify the right - angled triangle

The baseball diamond is a square with side length \(a = 90\) ft. The distance from the catcher (at home plate) to second base is the length of the diagonal of the square. In a square, the diagonal \(d\) and the sides form a right - angled triangle, where the two sides of the right - angled triangle have length \(a = 90\) ft.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem for a right - angled triangle is \(d^{2}=a^{2}+a^{2}\), where \(a = 90\) ft. Substituting \(a = 90\) into the formula, we get \(d^{2}=90^{2}+90^{2}=8100 + 8100=16200\).

Step3: Solve for \(d\)

Take the square root of both sides: \(d=\sqrt{16200}\). We can simplify \(\sqrt{16200}=\sqrt{8100\times2}=90\sqrt{2}\approx90\times1.414 = 127.26\) ft.

Answer:

\(90\sqrt{2}\approx127.26\) ft