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?

(10 points)
Responses

64 feet
64 feet

127 feet
127 feet

156 feet
156 feet

180 feet

Answer 1

To find the distance from home plate to second base on a baseball field, we can use the properties of a right triangle. The distance from home plate to first base and the distance from first base to second base creates a right angle along the baseline.

1. The distance from home plate to first base is 90 feet.
2. The distance from first base to second base is also 90 feet.

These two distances can be thought of as the legs of a right triangle, with the distance from home plate to second base being the hypotenuse.

Using the Pythagorean theorem:

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

where \( c \) is the hypotenuse (distance from home plate to second base), and \( a \) and \( b \) are the two legs (both 90 feet).

Substituting the values:

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

\[
c^2 = 8100 + 8100
\]

\[
c^2 = 16200
\]

Now, take the square root of both sides to find \( c \):

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

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

Therefore, the correct response is:

**127 feet**