Answer:
the length of the other leg is 4sqrt(24) yards. This can also be simplified as 8sqrt(6) yards.
Explanation:
Let's use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the legs (the other two sides).
In this problem, one leg has a length of 13 yards, and the hypotenuse has a length of 23 yards. Let's call the length of the other leg x.
Using the Pythagorean theorem, we get:
23^2 = 13^2 + x^2
Simplifying and solving for x, we get:
x^2 = 23^2 - 13^2
x^2 = 384
x = sqrt(384)
x = sqrt(16 * 24)
x = 4sqrt(24)
Therefore, the length of the other leg is 4sqrt(24) yards. This can also be simplified as 8sqrt(6) yards.