ABC is a right triangle, so by Pythagoras' theorem,
[tex]AB^2+AC^2=BC^2\implies BC=\sqrt{4^2+9^2}=\sqrt{97}[/tex]
Then by the law of sines,
[tex]\dfrac{\sin A}{BC}=\dfrac{\sin C}{AB}\iff\dfrac1{\sqrt{97}}=\dfrac{\sin C}4\implies\sin C=\dfrac4{\sqrt{97}}[/tex]
[tex]\implies C=\sin^{-1}\dfrac4{\sqrt{97}}\approx24^\circ[/tex]
