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 bail? Round your answer to the nearest tenth.
? feet
We can use the Pythagorean theorem to solve this problem. Since the field is square, the distance from the shortstop to first base is the same as the distance from the second base to first base. Let's call this distance x.
According to the Pythagorean theorem, we have:
x^2 = 30^2 + x^2
Simplifying the equation, we have:
2x^2 = 30^2
Dividing both sides by 2, we have:
x^2 = 30^2 / 2
Taking the square root of both sides, we have:
x = sqrt(30^2 / 2)
Calculating the value, we have:
x ≈ 21.2
Therefore, the shortstop needs to throw the ball approximately 21.2 feet to first base. Rounding to the nearest tenth, the answer is 21.2 feet.