Warehouse crane beneath a roof

A warehouse is \(18\text{ m}\) long and \(12\text{ m}\) wide, with vertical walls \(6\text{ m}\) high.

Its symmetric pitched roof has sloping edges \(7.5\text{ m}\) long in each end cross-section. The ridge is directly above the centre line of the warehouse.

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

1. Find the vertical height of the roof ridge above the ground.[2]
2. Find the distance from a bottom corner to the opposite top corner of the vertical walls.[3]
3. From the same bottom corner, find the angle of elevation of the ridge point at the opposite end.[3]