A shortstop is standing in the base path between second and third base when she fields the ball. She is 25 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 calculate the distance the shortstop needs to throw the ball, we first need to know the dimensions of the baseball diamond.
The regulation distance between bases on a baseball field for Major League Baseball is 90 feet. Thus, if we assume the field is square, that makes each side of the square 90 feet long.
The shortstop is 25 feet from second base, standing in the base path between second and third base. So she is 90 - 25 = 65 feet from third base.
Now, we will use the Pythagorean theorem to calculate the distance of the throw to first base. Since first base is diagonally across from third base, the distance from the shortstop to first base is the hypotenuse of a right triangle where one leg is the distance from the shortstop to third base (65 feet) and the other leg is the distance from third base to first base (90 feet, the length of one side of the square).
Using the Pythagorean theorem (a^2 + b^2 = c^2), where a and b are the legs of a right triangle and c is the hypotenuse:
a = 65 feet (distance from the shortstop to third base)
b = 90 feet (distance across the diamond from third to first base)
Let's calculate the length of the hypotenuse (c):
c^2 = a^2 + b^2
c^2 = 65^2 + 90^2
c^2 = 4225 + 8100
c^2 = 12325
Now, take the square root of both sides to solve for c:
c = √12325
c ≈ 111 feet
Therefore, the shortstop needs to make a throw of approximately 111 feet to first base. Since the question asks to round to the nearest tenth, the distance is approximately 111.0 feet.