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

180 feet
180 feet

156 feet
156 feet

64 feet
64 feet

127 feet

Answer 1

To find the distance from home plate to second base on a baseball field, we can use the Pythagorean theorem. In a standard baseball diamond, home plate, first base, and second base form a right triangle, with home plate to first base as one leg and first base to second base as the other leg.

The distance from home plate to first base is 90 feet, and the distance from first base to second base is also 90 feet (since all bases are 90 feet apart).

Let \( a \) be the distance from home plate to first base (90 feet), and \( b \) be the distance from first base to second base (90 feet). The distance from home plate to second base \( c \) can be calculated using the Pythagorean theorem:

\[
c^2 = a^2 + b^2
\]

Substituting the values:

\[
c^2 = 90^2 + 90^2
\]
\[
c^2 = 8100 + 8100
\]
\[
c^2 = 16200
\]

Taking the square root:

\[
c = \sqrt{16200} \approx 127.28
\]

Rounding to the nearest foot, the distance from home plate to second base is approximately 127 feet.

The correct answer is **127 feet**.