3
\(A B C\) is an object made from a uniform wire consisting of two straight portions \(A B\) and \(B C\), in which \(A B = a , B C = x\) and angle \(A B C = 90 ^ { \circ }\). When the object is freely suspended from \(A\) and in equilibrium, the angle between \(A B\) and the horizontal is \(\theta\) (see diagram).

1. Show that \(x ^ { 2 } \tan \theta - 2 a x - a ^ { 2 } = 0\).
2. Given that \(\tan \theta = 1.25\), calculate the length of the wire in terms of \(a\).