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?
64 feet
156 feet
127 feet
180 feet
64 feet
156 feet
127 feet
180 feet
Answers
GPT-4o mini
To find the distance from home plate to second base on a baseball field, we can visualize or use the Pythagorean theorem.
In a baseball field, the bases form a square. The distance from home plate to first base is 90 feet, and the distance from first base to second base is also 90 feet. Therefore, we can treat the path from home plate to second base as the hypotenuse of a right triangle, where each leg of the triangle is 90 feet.
Using the Pythagorean theorem:
\[
c = \sqrt{a^2 + b^2}
\]
where \(c\) is the distance from home plate to second base, and \(a\) and \(b\) are the distances from home plate to first base and first base to second base (both 90 feet).
Calculating:
\[
c = \sqrt{90^2 + 90^2} = \sqrt{8100 + 8100} = \sqrt{16200}
\]
Calculating \( \sqrt{16200} \):
\[
\sqrt{16200} \approx 127.3
\]
Rounding to the nearest foot gives us approximately 127 feet.
Thus, the distance from home plate to second base is **127 feet**.
In a baseball field, the bases form a square. The distance from home plate to first base is 90 feet, and the distance from first base to second base is also 90 feet. Therefore, we can treat the path from home plate to second base as the hypotenuse of a right triangle, where each leg of the triangle is 90 feet.
Using the Pythagorean theorem:
\[
c = \sqrt{a^2 + b^2}
\]
where \(c\) is the distance from home plate to second base, and \(a\) and \(b\) are the distances from home plate to first base and first base to second base (both 90 feet).
Calculating:
\[
c = \sqrt{90^2 + 90^2} = \sqrt{8100 + 8100} = \sqrt{16200}
\]
Calculating \( \sqrt{16200} \):
\[
\sqrt{16200} \approx 127.3
\]
Rounding to the nearest foot gives us approximately 127 feet.
Thus, the distance from home plate to second base is **127 feet**.