Final answer:
To calculate the diagonal distance a player travels across a soccer field, one can use the Pythagorean theorem. The field's dimensions create a right triangle, with the diagonal as the hypotenuse. The players travel approximately 166.4 meters when running diagonally across a field that is 100 meters wide and 133 meters long.
Step-by-step explanation:
The distance a soccer player travels when running diagonally across a field that is 100 meters wide and 133 meters long can be determined using the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the diagonal path the player runs forms the hypotenuse of a right-angled triangle, with the width and length of the soccer field as the other two sides.
To find the diagonal distance (D), we use the equation D² = width² + length². Plugging in the values:
D² = 100² + 133²
D² = 10,000 + 17,689
D² = 27,689
Taking the square root of both sides gives us:
D = √27,689
D = 166.4 meters (rounded to one decimal place)
Therefore, each player travels a distance of approximately 166.4 meters when running diagonally across the field.