Rescue craft around an offshore beacon

An offshore beacon is at \(O\). Rescue craft \(A\), \(B\) and \(C\) are on horizontal water.

\(OA=0.45\text{ km}\) on a bearing of \(032^\circ\) from \(O\), and \(OB=0.62\text{ km}\) on a bearing of \(118^\circ\) from \(O\).

Craft \(C\) is \(0.30\text{ km}\) west and \(0.80\text{ km}\) south of \(O\). The beacon tower is \(36\text{ m}\) high.

Give non-exact numerical answers correct to \(3\) significant figures.

1. Find \(AB\).[3]
2. Find the angle of depression from the top of the beacon tower to \(A\).[2]
3. Find the bearing of \(C\) from \(O\).[2]
4. A rescue launch travels directly from \(A\) to \(B\). Find its shortest distance from \(O\).[2]
5. It is claimed that triangle \(AOB\) is right-angled. Determine whether the claim is true, showing a calculation.[2]