Question

In a baseball field, the distance from the home plate to the first base is 115 feet. What is the distance from the home plate to the second base? Round to the nearest hundredth.

(1 point)
Responses

230.00 feet
230.00 feet

199.19 feet
199.19 feet

162.63 feet
162.63 feet

115.00 feet

Answer 1

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**