Given:
In triangle MNO,
[tex]\begin{gathered} n=88inches \\ m=60inches \\ \angle M=38\degree \end{gathered}[/tex]Required:
To find the angle N.
Explanation:
According to the sine rule
[tex]\frac{\sin M}{m}=\frac{\sin N}{n}[/tex]Now
[tex]\begin{gathered} \frac{\sin38}{60}=\frac{\sin N}{88} \\ \\ \frac{0.6156}{60}\times88=\sin N \\ \\ \sin N=0.9028 \\ \\ \angle N=\sin^{-1}(0.9028) \\ \\ \angle N=64.55\degree \end{gathered}[/tex]Or
[tex]\begin{gathered} \angle N=180-64.55 \\ =115.45\degree \end{gathered}[/tex]Final Answer:
The possible values of N are,
[tex]\angle N=64.5\degree,115.5\degree[/tex]