A shortstop 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.
The shortstop needs to throw the ball diagonally across the square field to reach first base. The distance from second base to first base is the same as the distance from third base to first base, so the throw is the diagonal of a square with sides 30 feet.
Using the Pythagorean theorem, the length of the diagonal (d) is found by adding the squares of the sides (30^2 + 30^2) and taking the square root of the sum.
d = √(30^2 + 30^2)
d = √(900 + 900)
d = √(1800)
d ≈ 42.4
Therefore, the shortstop needs to throw the ball approximately 42.4 feet to first base.