A square has four internal angles each measuring 90 degrees. One side of the square measures 90 feet. A dashed line divides the square in half diagonally across opposing vertices.
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
64 feet
64 feet
127 feet
127 feet
180 feet
180 feet
156 feet
The distance from home plate to second base can be calculated using the Pythagorean Theorem, since we have a right triangle with sides of 90 feet and 90 feet (because the dashed line divides the square in half diagonally).
Using the formula a^2 + b^2 = c^2, where a and b are the two sides of the triangle and c is the hypotenuse, we get:
90^2 + 90^2 = c^2
8100 + 8100 = c^2
16200 = c^2
c = √16200
c ≈ 127.28
Therefore, the distance from home plate to second base is approximately 127 feet. The nearest foot to this distance is 127 feet.
So, the correct response is:
127 feet