Teorema sinusului spune ca
[tex]\frac{AB}{\sin{C}}=\frac{AC}{\sin{B}}[/tex]
Atunci in cazul nostru
[tex]\frac{AB}{\sin{\frac{\pi}{4}}}=\frac{AC}{\sin{\frac{\pi}{6}}}\Rightarrow \frac{AB}{\frac{\sqrt{2}}{2}}=\frac{AC}{\frac{1}{2}}\Rightarrow \frac{AB}{\sqrt{2}}=AC\Rightarrow \frac{AB}{AC}=\sqrt{2}[/tex]
Atunci avem inegalitatea
[tex]AB<2AC\Rightarrow \frac{AB}{AC}<2\Rightarrow \sqrt{2}<2\Rightarrow 2<4[/tex] deci inegalitatea este adevarata
