What is the length of the marked segment?



The triangle \(ABC\) is a right triangle in \(C\), because it is the adjacent angle to a right angle, see or .
The segment \(AC\) has length \(\dfrac{2\sqrt{3}-3}{6}\), see .
The angle in \(B\) equals \(180^\circ - 90^\circ - 60^\circ = 30^\circ\). So we obtain the length of \(AB\) by \[AB =\dfrac{ \dfrac{2\sqrt{3}-3}{6}}{\sin 30^\circ} = \dfrac{2\sqrt{3}-3}{3} \,.\]