Final answer:
The side length of the square field with a diagonal of 212 meters is approximately 14991 cm, calculated using the Pythagorean theorem. The diagonal makes a 45-degree angle with the side, owing to the properties of a square.
Step-by-step explanation:
The student has inquired about the side length of a square field given the diagonal length. Since the field is square, we can use the Pythagorean theorem to find the side length. The Pythagorean theorem states that in a right-angled 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. For a square, the diagonal acts as the hypotenuse, and the sides of the square are equal in length.
Calculation of Side Length: If the diagonal (d) is 212 meters, then using the formula d = √(2 × s²), where s is the side length, we can rewrite this as s = √(d² / 2). Plugging in the numbers:
s = √(212² / 2)s ≈ √(44944 / 2)s ≈ √(22472)s ≈ 149.91 meters. When rounded to the nearest centimeter, it is approximately 14991 cm.
Angle Between Diagonal and Side: Since the field is a square, the angles between the sides and the diagonal are right angles, which are 45 degrees.