Will a lorry fit through a circular tunnel

The cross-section of a tunnel is part of a circle of radius \(5\) m. The road is a horizontal chord of the circle, \(8\) m wide, below the centre. Model a lorry's cross-section as a rectangle that drives along the middle of the road.

1. Find the height of the highest point of the tunnel above the road.[3]
2. A lorry is \(2.6\) m wide and \(6.8\) m tall. Determine whether it fits through the tunnel.[3]
3. A safety rule requires \(0.5\) m clearance above the top corners of a vehicle. Find the greatest width of a \(7\) m tall vehicle that meets the rule, and state one assumption of the model.[3]