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In the diagram, \(A B C\) is a triangle in which \(A B = 4 \mathrm {~cm} , B C = 6 \mathrm {~cm}\) and angle \(A B C = 150 ^ { \circ }\). The line \(C X\) is perpendicular to the line \(A B X\).
- Find the exact length of \(B X\) and show that angle \(C A B = \tan ^ { - 1 } \left( \frac { 3 } { 4 + 3 \sqrt { } 3 } \right)\).
- Show that the exact length of \(A C\) is \(\sqrt { } ( 52 + 24 \sqrt { } 3 ) \mathrm { cm }\).