Step-by-step explanation:
By the Law of Cosines,
[tex]l^{2}=5^{2}+9^{2}-2(5)(9)(\cos 43^{\circ})\\l^{2}=106-90 \cos 43^{\circ}\\l=\sqrt{106-90 \cos 43^{\circ}[/tex]
This means that by the Law of Sines,
[tex]\frac{\sin J}{9}=\frac{\sin 43^{\circ}}{\sqrt{106-90 \cos 43^{\circ}}}\\\sin J=9 \left(\frac{\sin 43^{\circ}}{\sqrt{106-90 \cos 43^{\circ}}} \right)\\J=\sin^{-1} \left(9\left(\frac{\sin 43^{\circ}}{\sqrt{106-90 \cos 43^{\circ}}} \right) \right)\\J \approx \boxed{75.55^{\circ}}[/tex]
