On the 45-45-90 triangle, the sides that are not the hypotenuse are equal lengths. This makes sense as the angles are equal. The equal lengths are why dividing a by b results in one and dividing either of them by c equals the same number, 0.7071067812. The length of c is the length of one of the sides times 1.414213562.
On this triangle, the 30-60-90, the short a side is 1/2 of the hypotenuse c. The length of b is always the same ratio when compared to a or c.