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In the diagram, triangle \(A B C\) is right-angled and \(D\) is the mid-point of \(B C\). Angle \(D A C = 30 ^ { \circ }\) and angle \(B A D = x ^ { \circ }\). Denoting the length of \(A D\) by \(l\),
- express each of \(A C\) and \(B C\) exactly in terms of \(l\), and show that \(A B = \frac { 1 } { 2 } l \sqrt { } 7\),
- show that \(x = \tan ^ { - 1 } \left( \frac { 2 } { \sqrt { } 3 } \right) - 30\).