The triangle described is shown below (this is not the correct triangle but we need something to help):
To find the lenght of side AC we need to use the law os cosines:
[tex]AC^2=AB^2+BC^2-2(AB)(BC)\cos B[/tex]In this case we have:
[tex]\begin{gathered} AC^2=12^2+18^2-2(12)(18)\cos 75 \\ AC^2=356.19 \\ AC=\sqrt[]{356.19} \\ AC=18.9 \end{gathered}[/tex]Now, to find angle A can use the law of sines:
[tex]\frac{\sin A}{BC}=\frac{\sin B}{AC}[/tex]Then:
[tex]\begin{gathered} \frac{\sin A}{18}=\frac{\sin 75}{18.9} \\ \sin A=\frac{18}{18.9}\sin 75 \\ A=\sin ^{-1}(\frac{18}{18.9}\sin 75) \\ A=66.9 \end{gathered}[/tex]Therefore the correct answer is A.
