Question

hidden pythagorean theorem

1. a professional baseball diamond has very strict rules for how it should be

laid out. how far is it from 1st base to 3rd base?

Explanation:

Step1: Identify the right - angled triangle

A baseball diamond is a square. The distance from \(1^{st}\) base to \(3^{rd}\) base is the diagonal of the square. Let the side length of the square (distance between consecutive bases) be \(a = 90\) feet. The diagonal \(d\) of a square forms a right - angled triangle with two sides of the square.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(d^{2}=a^{2}+a^{2}\). Substitute \(a = 90\) into the formula: \(d^{2}=90^{2}+90^{2}\).

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Answer:

It is approximately \(127.26\) feet from \(1^{st}\) base to \(3^{rd}\) base.