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 the distance the shortstop needs to throw the ball, we can model the baseball diamond as a square. Let's assume that the standard distance between bases on a baseball field is 90 feet. This means that each side of the square, which represents the distance between bases, is 90 feet long.
The shortstop is standing 25 feet from second base towards third base. We can form a right triangle by drawing a line from the shortstop's position to first base, with the two other sides being the paths from the shortstop to second base and first base to second base.
Given that the shortstop is 25 feet from second base, she is also 65 feet from third base because the total distance from second to third base is 90 feet (90 - 25 = 65 feet).
The hypotenuse of the right triangle will represent the distance of the throw from the shortstop to the first base. The two sides of the triangle will be:
1. The distance from the shortstop to second base: 65 feet straight towards third base.
2. The distance from second base to first base: 90 feet.
Now we apply the Pythagorean theorem to find the distance of the throw (hypotenuse). The theorem states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):
c² = a² + b²
Plugging in the sides:
c² = 65² + 90²
c² = 4225 + 8100
c² = 12325
Now we take the square root to find the throw distance:
c = √12325
c ≈ 111 feet
So the shortstop needs to throw the ball approximately 111 feet to reach first base. Rounding to the nearest tenth, the answer is 111.0 feet.