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?
(2 points)
156 feet
127 feet
180 feet
64 feet
(2 points)
156 feet
127 feet
180 feet
64 feet
Answers
GPT-4o mini
To find the distance from home plate to second base on a baseball field, we can use the properties of a right triangle. The baseball diamond forms a square with each side being 90 feet (the distance from home plate to first base and from first base to second base).
The distance from home plate to second base is the diagonal of this square. To calculate it, we can use the Pythagorean theorem:
\[
d = \sqrt{(a^2 + b^2)}
\]
where \( a \) and \( b \) are both the lengths of the sides of the square (which are 90 feet):
\[
d = \sqrt{(90^2 + 90^2)} = \sqrt{(8100 + 8100)} = \sqrt{16200}
\]
Calculating this gives:
\[
d = \sqrt{16200} \approx 127.28
\]
Rounding this to the nearest foot, we get the distance from home plate to second base is **127 feet**.
The distance from home plate to second base is the diagonal of this square. To calculate it, we can use the Pythagorean theorem:
\[
d = \sqrt{(a^2 + b^2)}
\]
where \( a \) and \( b \) are both the lengths of the sides of the square (which are 90 feet):
\[
d = \sqrt{(90^2 + 90^2)} = \sqrt{(8100 + 8100)} = \sqrt{16200}
\]
Calculating this gives:
\[
d = \sqrt{16200} \approx 127.28
\]
Rounding this to the nearest foot, we get the distance from home plate to second base is **127 feet**.