I need help on geometry proofs

The hypotenuse has got to have the longest side in a right angled triangle.Say, A=Adjacent, O=Opposite, H=HypotenuseA²+O²=H²Therefore,A²<H²O²<H²As this is the case:H>AH>O

Other proof:Look at the picture.[tex]sin\alpha\in (0;\ 1)\\\\sin\alpha=\frac{b}{h} < 1\ therefore\ h > b\\\\cos\alpha\in(0;\ 1)\\\\cos\alpha=\frac{a}{h} < 1\ therefore\ h > a\\\\the\ conclusion:\ h > a\ and\ h > b\ \Rightarrow h\ has\ to\ be\ the\ longest\ side\\of\ a\ right\ triangle.[/tex]