[tex] \frac{a}{sin A} = \frac{b}{sin B}
\\ \\ \frac{78}{sin28^{o}}= \frac{103}{sin B}
\\ \\ sin B= \frac{103*sin28^{o}}{78} =0.6199
\\ \\ B=arcsin(0.6199), B=38.3^{o}, or B=180-38.3=141.7
First triangle:
a=78, A=28^{o}, b=103, B=38.3^{o}, c=163.2, C=113.7
C=180-28-38.3=113.7^{o},
\\ \\ \frac{a}{sin A} = \frac{c}{sin C}, \frac{78}{sin28^{o}}= \frac{c}{sin 113.7^{o}}
\\ \\ c= \frac{78*sin113.7^{o}}{sin28^{o}} = 163.2
[/tex]
[tex]Second// triangle:
a=78, A=28^{o}, b=103, B=141.7^{o}, c=29.7, C=10.3^{o}
\\ \\ C=180-141.7-28=10.3^{o}
\\ \\ \frac{a}{sin A} = \frac{c}{sin C}
\\ \\ \frac{78}{sin 28} = \frac{c}{sin 10.3}
\\ \\\ c= \frac{78*sin10.3}{sin28} = 29.7[/tex]
