IB Math HL Trigonometry Test 5 2016 P2 Q7

A tank is a regular square pyramid with apex \(O\) downwards. Its square base \(ABCD\) has side \(6\text{ m}\), and the perpendicular depth is \(3\sqrt2\text{ m}\).

1. Show that triangle \(OAB\) is equilateral.[4]
2. Two ants run from \(O\) towards \(A\) and \(B\) at \(1.5\text{ cm s}^{-1}\) and \(2\text{ cm s}^{-1}\), respectively. Find their separation after \(40\) seconds.[5]