Answer: \(51{\circ}\)
Step-by-step explanation:
The law of sines says that in a triangle ABC with sides a,b and c respectively we have :-
\(\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\)
Now , for the given triangle in the picture we have
\(\frac{\sin 104^{\circ}}{15}=\frac{\sin J}{12}\\\\\Rightarrow \sin J=\frac{\sin 104^{\circ}\times12}{15}\\\\\Rightarrow \sin J=\frac{0.97029572627\times12}{15}\\\\\Rightarrow \sin J=0.776236581016\\\\\Rightarrow J=\sin^{-1}(0.776236581016)=50.91728017\approx51{\circ}..............[\text{Using calculator}]\)
Hence, the measure of angle J = \(51{\circ}\)
