In a baseball field, the bases form a square with each side measuring 115 feet. The distance from home plate to second base is the diagonal of this square.
To calculate the diagonal \(d\) of a square, you can use the Pythagorean theorem:
\[ d = \sqrt{a^2 + a^2} = \sqrt{2a^2} = a\sqrt{2} \]
where \(a\) is the length of one side. In this case, \(a = 115\) feet.
Now, calculate the distance:
\[ d = 115\sqrt{2} \approx 115 \times 1.41421356 \approx 162.63 \text{ feet} \]
Thus, the distance from home plate to second base is approximately 162.63 feet. So the correct response is:
162.63 feet