A short stop is standing in the base path between second and third base when she fields the ball. She is 30 feet from second base and needs to make the throw to first base. Assuming the field is square, how far does she need to throw the ball? Round your answer to the nearest tenth.
To find the distance the shortstop needs to throw the ball, we need to determine the length of the diagonal of the square field.
Since the field is square, the distance from second base to home plate is the same as the distance from first base to third base.
So, the distance from second base to home plate is 90 feet (3 bases x 30 feet/base) and the distance from first base to third base is also 90 feet.
We can use the Pythagorean theorem to find the length of the diagonal. Let's call it "d".
Using the formula c^2 = a^2 + b^2, where "c" is the length of the diagonal (d), and "a" and "b" are the sides of the square field (90 feet):
d^2 = 90^2 + 90^2
d^2 = 8100 + 8100
d^2 = 16200
To solve for "d", take the square root of both sides:
d ≈ √(16200)
d ≈ 127.28 feet
Therefore, the shortstop needs to throw the ball approximately 127.3 feet to reach first base, rounded to the nearest tenth.