In a baseball field, the bases form a square. The distance from home plate to first base is one side of the square, and the distance from home plate to second base is the diagonal.
To find the distance from home plate to second base, we can use the Pythagorean theorem.
Let \( a = 115 \) feet (the distance from home plate to first base) and \( b = 115 \) feet (the distance from home plate to third base). The distance \( d \) from home plate to second base (the diagonal) can be calculated as:
\[ d = \sqrt{a^2 + b^2} \]
Substituting the values:
\[ d = \sqrt{115^2 + 115^2} \]
Calculating \( 115^2 \):
\[ 115^2 = 13225 \]
So:
\[ d = \sqrt{13225 + 13225} = \sqrt{26450} \]
Calculating \( \sqrt{26450} \):
\[ d \approx 162.63 \text{ feet} \]
Thus, the distance from home plate to second base is approximately 162.63 feet.
The correct response is:
162.63 feet