解:∵在?$ABC$?中,?$∠B=90°$?
①當(dāng)?$AC=4,$??$BC=3$?時(shí),?$AB=\sqrt{AC2-BC2}=\sqrt{7}$?
?$sin C =\frac {AB}{AC}=\frac {\sqrt{7}}{4}$?
②當(dāng)?$AB=3,$??$BC=4$?時(shí),?$AC=\sqrt{AB2+BC2}=5$?
?$sin C=\frac {AB}{AC}=\frac {3}{5}$?
綜上,最小角的正弦值為?$\frac {\sqrt 7}4$?或?$\frac 35$?