Sagot :
The hypotenuse has got to have the longest side in a right angled triangle.
Say, A=Adjacent, O=Opposite, H=Hypotenuse
A²+O²=H²
Therefore,
A²<H²
O²<H²
As this is the case:
H>A
H>O
Say, A=Adjacent, O=Opposite, H=Hypotenuse
A²+O²=H²
Therefore,
A²<H²
O²<H²
As this is the case:
H>A
H>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]
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]