Here we have a direct application of the Law of Sines. Side a is opposite to angle 150°, while the side measuring 10 cm is opposito the the angle 12°. So, applying the Law of Sines:
[tex]\begin{gathered} \frac{\sin150\degree}{a}=\frac{\sin 12\degree}{10} \\ 10\sin 150\degree=a\sin 12\degree \\ a=\frac{10\sin150\degree}{\sin12\degree}=\frac{10\cdot0.5}{0.20791169\ldots}=24.0486\ldots\approx24.0 \end{gathered}[/tex]
So, the measure of a is approximately 24.0 cm.
