$ABCD$ is a uniform lamina with $AB = 1.8{\text{ }}m$, $AD = DC = 0.9{\text{ }}m$, and $AD$ perpendicular to $AB$ and $DC$ (see diagram).
a) Find the distance of the centre of mass of the lamina from $AB$ and the distance from $AD$.
The lamina is freely suspended at $A$ and hangs in equilibrium.
b) Calculate the angle between $AB$ and the vertical.

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