A designer is planning a pavilion with a square-based roof shaped as a right pyramid. The apex $A$ is vertically above the centre $O$ of the square base. Each side of the base is $8.4\text{ m}$ and the current vertical height $AO$ is $4.60\text{ m}$ The design requires the angle between each sloping edge and the plane of the base to be at least $38^\circ$ Let $P$ be a corner of the base.