Right hand.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

We can create an imaginary right triangle where the two short sides represent the distance between a person's left and right hands and the hypotenuse represents the distance between that person's left and right hands across the chest.

If we assume that the distance between a person's left and right hands is equal to the width of their chest, then we can calculate the length of each short side of the imaginary triangle as half this distance.

Let's say the distance between a person's left and right hand is 60 centimeters. Then the length of each short side of the imaginary triangle is equal to 30 centimeters.

Now we can apply the Pythagorean theorem to calculate the length of the hypotenuse of the imaginary triangle:

side length = √(short side length 1^2 + short side length 2^2)

hypotenuse length = √(30^2 + 30^2)

hypotenuse length = √(1800)

hypotenuse length ≈ 42.43

This means that the distance between a person's left and right hand across the chest is approximately 42.43 centimeters. Since a person's left and right hands are on opposite sides of the chest, the Pythagorean theorem thus proves that a person's left hand is on the left and a person's right hand is on the right. This is because the shorter sides of the triangle, which represent the distance between a person's hands, lie on the left and right sides of the hypotenuse, corresponding to the position of a person's left and right hands.