Question

a major league baseball \diamond\ is actually a square, 90 feet on a side (so what is the distance directly from home plate to second base (the diagonal of the square))? the distance directly from home plate to second base is approximately \\(\square\\) feet. (type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Apply Pythagorean theorem

For a square with side length $s$, diagonal $d = \sqrt{s^2 + s^2}$

Step2: Substitute $s=90$ feet

$d = \sqrt{90^2 + 90^2} = \sqrt{2\times90^2} = 90\sqrt{2}$

Step3: Calculate decimal value

$90\sqrt{2} \approx 90\times1.4142 = 127.278$

Step4: Round to two decimals

Round $127.278$ to two decimal places

Answer:

127.28