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\includegraphics[max width=\textwidth, alt={}, center]{3e7472a8-df1e-45c4-81fb-e4397bddf5ad-3_590_754_1425_699} A uniform lamina of weight 9 N has dimensions as shown in the diagram. The lamina is freely hinged to a fixed point at \(A\). A light inextensible string has one end attached to \(B\), and the other end attached to a fixed point \(C\), which is in the same vertical plane as the lamina. The lamina is in equilibrium with \(A B\) horizontal and angle \(A B C = 150 ^ { \circ }\).

1. Show that the tension in the string is 12.2 N .
2. Find the magnitude of the force acting on the lamina at \(A\).