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A uniform triangular lamina \(A B C\) is right-angled at \(B\) and has sides \(A B = 0.6 \mathrm {~m}\) and \(B C = 0.8 \mathrm {~m}\). The mass of the lamina is 4 kg . One end of a light inextensible rope is attached to the lamina at \(C\). The other end of the rope is attached to a fixed point \(D\) on a vertical wall. The lamina is in equilibrium with \(A\) in contact with the wall at a point vertically below \(D\). The lamina is in a vertical plane perpendicular to the wall, and \(A B\) is horizontal. The rope is taut and at right angles to \(A C\) (see diagram). Find
- the tension in the rope,
- the horizontal and vertical components of the force exerted at \(A\) on the lamina by the wall.