5
\includegraphics[max width=\textwidth, alt={}, center]{73f73a7a-79d0-40fc-8c6d-1e46dacda788-08_579_987_292_539} A uniform lamina is in the form of a triangle \(O B C\), with \(O C = 18 a , O B = 24 a\) and angle \(C O B = 90 ^ { \circ }\). The point \(A\) on \(O B\) is such that \(O A = x\) (see diagram). The triangle \(O A C\) is removed from the lamina.

1. Find, in terms of \(a\) and \(x\), the distance of the centre of mass of the remaining object \(A B C\) from \(O C\). [3]
   \includegraphics[max width=\textwidth, alt={}, center]{73f73a7a-79d0-40fc-8c6d-1e46dacda788-08_2718_40_141_2010}
   The object \(A B C\) is suspended from \(C\) .In its equilibrium position,the side \(A B\) makes an angle \(\theta\) with the vertical,where \(\tan \theta = \frac { 6 } { 5 }\) .
2. Find \(x\) in terms of \(a\) .