Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
JL = 2.7 units
JK = 4.7 units
∠L = 150°
Using Law of sines,
[tex]\frac{\sin L}{L}=\frac{\sin K}{K}=\frac{\sin J}{J}\\\frac{\sin 105^\circ}{4.7}=\frac{\sin K}{2.7}\\\\\frac{\sin 105^\circ\times 2.7}{4.7}=\sin K\\\\0.5548=\sin K\\\\\sin^{-1}(0.5548)=K\\\\33.7^\circ=K[/tex]
Now, using "Sum of interior angles of a triangle is supplementary."
[tex]\angle J+\angle K+\angle L=180^\circ\\\\\angle J+33.7^\circ+105^\circ=180^\circ\\\\\angle J+138.7^\circ=180^\circ\\\\\angle J=180^\circ-138.7^\circ\\\\\angle J=41.3^\circ[/tex]
Again by using "Law of sines" we get,
[tex]\frac{\sin L}{L}=\frac{\sin K}{K}=\frac{\sin J}{J}\\\\\frac{\sin 105^\circ}{4.7}=\frac{\sin 41.3^\circ}{J}\\\\J=\frac{\sin 41.3^\circ \times 4.7}{\sin 105^\circ}\\\\J=3.211\\\\J=3.2\ approx.[/tex]
Hence, Third option is correct.
