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 find out how far the shortstop needs to throw the ball to first base, we need to determine the distance between where she is on the field and first base. We'll use the Pythagorean theorem to calculate this, which states that in a right-angle 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 lengths of the other two sides.
Assuming a regulation baseball infield where the bases are 90 feet apart, the diamond they form is a square. The shortstop is 25 feet from second base, meaning she is standing 90 - 25 = 65 feet away from third base along the base path.
We need to find the diagonal distance from where the shortstop is to first base, which is the hypotenuse of a right-angled triangle. One leg of this triangle is from the shortstop along the base path to third base (65 feet), and the other leg is the distance from third base straight to first base (which is 90 feet, the distance between bases).
Using the Pythagorean theorem:
distance^2 = side1^2 + side2^2
distance^2 = 65^2 + 90^2
distance^2 = 4225 + 8100
distance^2 = 12325
Taking the square root to find the distance:
distance = √12325
distance ≈ 111.0
So, the shortstop needs to throw the ball approximately 111.0 feet to get the ball to first base. We can round the answer to the nearest tenth, but in this case, 111.0 is already at one decimal place.