Answer: (A) \(30^\circ\)
\[AB^2 + BC^2 = 108 + 36 = 144 = AC^2\]So by the converse of Pythagoras theorem, \(\angle B = 90^\circ\) and AC is the hypotenuse.
BC = 6 is half of the hypotenuse AC = 12, so the angle opposite BC, i.e. \(\angle A\), is \(30^\circ\) (property of the \(30^\circ\)–\(60^\circ\)–\(90^\circ\) triangle).