Can I infer the hypotenuse given only $a > b$?

Question

Today, I came up with a problem. The problem is this:

Let $a$, $b$ and $c$ be the sides of a right-angled triangle, such that $a > b$. The nature of $c$ is unknown. Can I infer the hypotenuse given only this data?

Resolution:
The sides of all right triangles should follow: $$ hypt \gt adj1 \ge adj2 $$ Where $adj1$ and $adj2$ are the remaining, adjacent sides. I then do a simple permutation of the hypotenuse within the above to uncover all the possibilities:

Possibility 1. $$ a (hypt) \gt b(adj1, adj2) \ge c (adj1, adj2) $$
Possibility 2. $$ a (adj1, adj2) \lt b (hypt) $$ $$ b (hypt) \gt c (adj1, adj2) $$
Possibility 3. $$ a (adj1, adj2) \le b(adj1, adj2) \lt c(hypt) $$

Is this correct?

Answer 1

Given a right-angled triangle with $a>b$, there are 3 possibilities:

$$a> b\geq c\\ a> c\geq b\\ c> a > b .$$

$a$ is the hypotenuse in the first two cases; $c$ is the hypotenuse in the last case.