4. The diagram below shows a uniform rod \(A B\), of weight 10 N , hinged to a vertical wall at \(A\). The rod is held in a horizontal position by means of a light inextensible string. One end of the string is attached to a point \(C\) on the rod and the other end is attached to a point \(D\) on the wall. The point \(D\) is 0.6 m vertically above \(A\) and the length of \(A C\) is 0.8 m . A particle of weight 25 N is attached to the rod at \(B\) and the tension in the string is 75 N .
\includegraphics[max width=\textwidth, alt={}, center]{b9c63cb4-d446-4548-be42-e30b10cb4b99-4_572_808_612_625}

1. Find the length of the rod \(A B\).
2. Calculate the magnitude and direction of the reaction at the hinge at \(A\).