Question
Matt is the catcher for his school's baseball team. The catcher must be able to throw from home plate to second base. What is the distance from home plate to second base? second base 90 ft 90 ft third base first base 1 90 ft 1 90 ft home plate A. 90 ft B. 90 /2ft C. 180 D. 180~/2ft
Answers
GPT-4o mini
To find the distance from home plate to second base on a baseball diamond, we can visualize the diamond as a square where each side (from home plate to first base, first base to second base, second base to third base, and third base back to home plate) is 90 feet.
When throwing from home plate to second base, you are effectively dividing the square into two right triangles. The distance from home plate to second base is the hypotenuse of a right triangle where both legs are equal to the distance from home plate to first base (90 ft) and first base to second base (90 ft).
Using the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]
where \(c\) is the hypotenuse, and \(a\) and \(b\) are the legs of the triangle (both 90 ft in this case).
\[
c^2 = 90^2 + 90^2
\]
\[
c^2 = 8100 + 8100
\]
\[
c^2 = 16200
\]
\[
c = \sqrt{16200}
\]
\[
c = 90\sqrt{2} \, \text{feet}
\]
Thus, the distance from home plate to second base is \(90\sqrt{2}\) feet.
From your options, the correct choice is:
**D. \(180/\sqrt{2}\, \text{ft}\)** (which simplifies to \(90\sqrt{2}\, \text{ft}\)).
When throwing from home plate to second base, you are effectively dividing the square into two right triangles. The distance from home plate to second base is the hypotenuse of a right triangle where both legs are equal to the distance from home plate to first base (90 ft) and first base to second base (90 ft).
Using the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]
where \(c\) is the hypotenuse, and \(a\) and \(b\) are the legs of the triangle (both 90 ft in this case).
\[
c^2 = 90^2 + 90^2
\]
\[
c^2 = 8100 + 8100
\]
\[
c^2 = 16200
\]
\[
c = \sqrt{16200}
\]
\[
c = 90\sqrt{2} \, \text{feet}
\]
Thus, the distance from home plate to second base is \(90\sqrt{2}\) feet.
From your options, the correct choice is:
**D. \(180/\sqrt{2}\, \text{ft}\)** (which simplifies to \(90\sqrt{2}\, \text{ft}\)).