Final answer:
The length of the hypotenuse of a right triangle can be determined using the Pythagorean theorem. In this case, both legs of the right triangle are congruent and have a length of 23.6 yards. The length of the hypotenuse is approximately 47.1 yards (rounded to the nearest tenth).
Step-by-step explanation:
The length of the hypotenuse of a right triangle can be determined using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the legs (a and b). This can be expressed as a² + b² = c².
In this case, both legs of the right triangle are congruent and have a length of 23.6 yards. So, we can substitute a = b = 23.6 into the Pythagorean theorem and solve for c:
c² = a² + b² = (23.6)² + (23.6)² = 1110.56 + 1110.56 = 2221.12
c = √2221.12 = 47.1
Therefore, the length of the hypotenuse is approximately 47.1 yards (rounded to the nearest tenth).