In a baseball field, the configuration can be considered as a square with each side representing the base paths. The distance from home plate to first base is 115 feet.
To find the distance from home plate to second base, we can think of this in terms of the right triangle formed by home plate, first base, and second base. The distance from home plate to second base is the hypotenuse of this triangle, where each leg of the triangle represents the distance from home plate to first base and from first base to second base, both of which equal 115 feet.
Using the Pythagorean theorem:
\[ c = \sqrt{a^2 + b^2} \]
where \( a = 115 \) feet and \( b = 115 \) feet.
Substituting the values:
\[ c = \sqrt{115^2 + 115^2} \]
Calculating \( 115^2 \):
\[ 115^2 = 13225 \]
Now, substituting this back into the equation:
\[ c = \sqrt{13225 + 13225} = \sqrt{26450} \]
Calculating \( \sqrt{26450} \):
\[ c \approx 162.56 \text{ feet} \]
Rounding it to the nearest hundredth:
\[ c \approx 162.56 \text{ feet} \]
So, based on the options provided, the closest would be:
162.63 feet.