Answer
AB=6+6$\sqrt 3$$\approx$16.39
Work Step by Step
Draw an altitude from point C to a point on AB that we'll name M.
2CM=BC
2CM=12
CM=6
MB=CM$\sqrt 3$
MB=6$\sqrt 3$
AM=CM
AM=6
AB=AM+MB
AB=6+6$\sqrt 3$$\approx$16.39
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