A shortstop is standing in the base path between second and third base when she fields 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. Explain.
The shortstop is standing in the base path between second and third base, which means she is standing on a diagonal line that is perpendicular to the line connecting first and second base.
Using the Pythagorean theorem, we can find the distance she needs to throw the ball. The distance from second base to first base is the hypotenuse of a right triangle, with the distance of the shortstop from second base as one side and the distance from first base to the shortstop as the other side.
Let the distance from the shortstop to second base be x. The distance from second base to first base is also x (since the field is square), and the distance from the shortstop to first base is the hypotenuse.
By the Pythagorean theorem, the hypotenuse is √(x^2 + x^2) = √(2x^2) = x√2.
Since the distance from the shortstop to second base is 30 feet, the distance from the shortstop to first base is 30√2 feet.
Rounding to the nearest tenth, the shortstop needs to throw the ball approximately 42.4 feet.