Slant edge and vertex angle of a rectangular-based pyramid, and the distance between two points moving along its edges

A right pyramid \(VABCD\) has a horizontal rectangular base \(ABCD\) with \(AB=8\text{ m}\) and \(BC=6\text{ m}\). The vertex \(V\) is vertically above the centre of the base, at a height of \(12\text{ m}\) above it.

1. Show that \(VA=13\text{ m}\) and that \(\cos\angle AVB=\frac{137}{169}\).[4]
2. Two small robots leave \(V\) at the same instant. One moves along the edge \(VA\) at a constant speed of \(0.25\text{ m s}^{-1}\), and the other moves along the edge \(VB\) at a constant speed of \(0.3\text{ m s}^{-1}\). Find the distance between the robots \(20\) seconds later.[5]