Using Pythagorean theorem we can find AC:
[tex]AC = \sqrt{12^2-6^2} = \sqrt{108} = 6\sqrt{3}[/tex]
In right triangle, the tangent is defined as the ratio of the opposite side to the adjacent side. This is:
tan 60 = opposite side / adjacent side
tan 60 = 6√3 / 6
tan 60 = √3
