Let's consider the properties of a 45-45-90 triangle.
In a 45-45-90 triangle, the two non-right angles are both 45 degrees. This specific triangle is a type of isosceles right triangle where the two legs are congruent, meaning they have the same length.
The hypotenuse of such a triangle is longer than the legs, specifically by a factor of [tex]\(\sqrt{2}\)[/tex]. However, when comparing the lengths of the legs to each other, since they are both congruent:
1. Let’s denote the length of each leg as [tex]\(a\)[/tex].
2. Since both legs have the same length, the ratio of the length of one leg to the length of the other leg is simply [tex]\(a : a\)[/tex].
By simplifying [tex]\(a : a\)[/tex], we get [tex]\(1 : 1\)[/tex].
Thus, the ratio of the length of one leg to the length of the other leg in a 45-45-90 right triangle is:
[tex]\[ \boxed{1:1} \][/tex]
