In baseball, the length of the path between each pair of consecutive bases is 90 feet. The paths form right angles. How far does the ball need to travel if it is thrown from home plate directly to second base?

A.
90 feet
B.
127.3 feet
C.
135.7 feet
D.
180 feet

90^2 + 90^2 = 16,200^2

Square root of 16,200 = 127.3 feet

127.3

In baseball, the length of the path between each pair of consecutive bases is 90 feet. The paths form right angles. How far does the ball need to travel if it is thrown from home plate directly to second base?

127.3

90*90+90*90=16,200*16,200
Then you need to find the square root of 16,200, which would be 127.3

To find how far the ball needs to travel if it is thrown from home plate directly to second base, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, we can treat the distance from home plate to second base as the hypotenuse of a right triangle, with each base path forming one of the other two sides. Since each base path is 90 feet long and they form right angles, we have a right triangle with sides of length 90 feet.

Using the Pythagorean theorem, we can find the length of the hypotenuse:

hypotenuse^2 = first side^2 + second side^2
hypotenuse^2 = 90^2 + 90^2
hypotenuse^2 = 8100 + 8100
hypotenuse^2 = 16200

Taking the square root of both sides, we get:

hypotenuse = √16200
hypotenuse ≈ 127.3 feet

Therefore, the ball needs to travel approximately 127.3 feet if it is thrown from home plate directly to second base. The answer is option B: 127.3 feet.