The batter is now 90 feet away from the catcher. When the batter runs from home plate to 1st base, he covers 90 feet. When he makes a 90-degree turn to run to 2nd base, he forms a right triangle with sides of 90 feet each. In a right triangle, the hypotenuse (the side opposite the right angle) can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, if we let the distance from 1st base to home plate be one side of the right triangle (90 feet) and the distance from 2nd base to home plate be the other side (90 feet), then the distance from 1st base to 2nd base (the hypotenuse) can be calculated as follows:
(90 feet)^2 + (90 feet)^2 = (distance from 1st base to 2nd base)^2
8100 + 8100 = (distance from 1st base to 2nd base)^2
16200 = (distance from 1st base to 2nd base)^2
√16200 = distance from 1st base to 2nd base
√(9 x 1800) = distance from 1st base to 2nd base
√9 x √1800 = distance from 1st base to 2nd base
3 x √1800 = distance from 1st base to 2nd base
3 x 42.43 = distance from 1st base to 2nd base
127.29 feet = distance from 1st base to 2nd base
Therefore, the batter is now 90 feet + 127.29 feet = 217.29 feet away from the catcher.
