Question
The image shows a baseball field, where the distance from home plate to first base is 90 feet. What is the distance from home plate to second base to the nearest foot? (1 point) Responses 64 feet 64 feet 180 feet 180 feet 156 feet 156 feet 127 feet
Answers
GPT-4o mini
In a baseball field, the distance from home plate to second base can be calculated using the properties of a right triangle. The path from home plate to first base and from first base to second base forms a right triangle where both legs are 90 feet.
The distance from home plate to second base can be found using the Pythagorean theorem:
\[
c = \sqrt{a^2 + b^2}
\]
where \(a\) and \(b\) are both 90 feet (the distances from home plate to first base and from first base to second base).
Calculating it:
\[
c = \sqrt{90^2 + 90^2} = \sqrt{8100 + 8100} = \sqrt{16200}
\]
Calculating the square root:
\[
\sqrt{16200} \approx 127.28 \text{ feet}
\]
Rounding to the nearest foot, the distance from home plate to second base is approximately **127 feet**.
The distance from home plate to second base can be found using the Pythagorean theorem:
\[
c = \sqrt{a^2 + b^2}
\]
where \(a\) and \(b\) are both 90 feet (the distances from home plate to first base and from first base to second base).
Calculating it:
\[
c = \sqrt{90^2 + 90^2} = \sqrt{8100 + 8100} = \sqrt{16200}
\]
Calculating the square root:
\[
\sqrt{16200} \approx 127.28 \text{ feet}
\]
Rounding to the nearest foot, the distance from home plate to second base is approximately **127 feet**.