Answer:
[tex]12\sqrt[]{2}[/tex]
Explanation:
To be able to find AC, we 1st of all need to find CD.
Using trig ratios, let's go ahead and determine what the value of CD is;
[tex]\begin{gathered} \sin 45=\frac{CD}{12} \\ CD=12\sin 45 \\ \therefore CD=12\ast\frac{\sqrt[]{2}}{2}=6\sqrt[]{2} \end{gathered}[/tex]
Since we know CD, let's go ahead and find AC;
[tex]\begin{gathered} \sin 30=\frac{6\sqrt[]{2}}{AC} \\ AC\sin 30=6\sqrt[]{2} \\ AC=\frac{6\sqrt[]{2}}{\sin 30}=\frac{6\sqrt[]{2}}{\frac{1}{2}}=6\sqrt[]{2}\ast\frac{2}{1}=12\sqrt[]{2} \end{gathered}[/tex]
