3 A uniform ladder \(P Q\), of length 8 metres and mass 28 kg , rests in equilibrium with its foot, \(P\), on a rough horizontal floor and its top, \(Q\), leaning against a smooth vertical wall. The vertical plane containing the ladder is perpendicular to the wall and the angle between the ladder and the floor is \(69 ^ { \circ }\). A man, of mass 72 kg , is standing at the point \(C\) on the ladder so that the distance \(P C\) is 6 metres. The man may be modelled as a particle at \(C\).
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1. Draw a diagram to show the forces acting on the ladder.
2. With the man standing at the point \(C\), the ladder is on the point of slipping.
   1. Show that the magnitude of the reaction between the ladder and the vertical wall is 256 N , correct to three significant figures.
   2. Find the coefficient of friction between the ladder and the horizontal floor.