We are given some information about a triangle, and with the information that we have we can solve this in 2 ways: using the cosine of angle C, or the sine of angle A, an angle which we know measures 60° because the sum of the internal angles of a triangle must be 180°. Let's use the second one:
We know that the sine of an angle is:
[tex]\begin{gathered} sin=\frac{opposite\text{ }side}{hypothenuse} \\ Therefore: \\ sin(60)=\frac{6}{AC} \\ 0.8660=\frac{6}{AC} \\ AC=\frac{6}{0.8660} \\ AC=6.92 \end{gathered}[/tex]
And by calculating 4√3 we know that it is 6.92, therefore, the correct answer is option A
