We use the Sine law because 2 angles and one side are known.
A= 150 degrees
a = ?
B = 12 degrees
b = 10cm
C =180 - 150 - 12 = 18 degrees
c = ?
[tex]\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} \\ \frac{\sin 150}{a}=\frac{\sin 12}{10}=\frac{\sin 18}{c} \\ \text{Crossmultiplying,} \\ c=\frac{10\sin 18}{\sin 12}=14.86 \end{gathered}[/tex]Therefore, to the nearest tenth, c = 14.9cm
