Question

a little league baseball \diamond\ is actually a square, 60 feet on a side (see the figure). what is the distance directly from first base to third base (the diagonal of the square)? the distance directly from first base to third base is approximately feet. (type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Apply Pythagorean theorem

In a square with side - length \(a = 60\) feet, if the diagonal is \(d\), by the Pythagorean theorem \(d^{2}=a^{2}+a^{2}\) for a right - triangle formed by two sides of the square. Here, \(a = 60\), so \(d^{2}=60^{2}+60^{2}\).

Step2: Calculate \(d^{2}\)

\(d^{2}=3600 + 3600=7200\).

Step3: Find \(d\)

\(d=\sqrt{7200}\). Simplifying, \(d = 60\sqrt{2}\approx60\times1.414214 = 84.85284\approx84.85\) feet.

Answer:

84.85