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\includegraphics[max width=\textwidth, alt={}, center]{43ed8ec7-67f1-418a-8d4e-ee96448647fd-3_441_450_213_808} Two uniform rods \(A B\) and \(B C\), each of length \(2 L \mathrm {~m}\) and of weight 84.5 N , are freely jointed at \(B\), and \(A B\) is freely jointed to a fixed point at \(A\). The rods are held in equilibrium in a vertical plane by a light string attached at \(C\) and perpendicular to \(B C\). The rods \(A B\) and \(B C\) make angles \(\alpha\) and \(\beta\) to the horizontal, respectively (see diagram). It is given that \(\cos \beta = \frac { 12 } { 13 }\).

1. Find the tension in the string.
2. Hence show that the force acting on \(B C\) at \(B\) has horizontal component of magnitude 15 N and vertical component of magnitude 48.5 N , and state the direction of the component in each case.
3. Find \(\alpha\).