Dock tide level after an overnight high tide

At a dock, the tide reaches a high of \(2.8\) metres at 6 pm on 5 September 2026. The next high tide occurs at 6 am on 6 September. The mean tide level is \(1.9\) metres.

Let \(t\) be the number of hours after midnight on 5 September 2026. The tide level \(L(t)\), in metres, is modelled by \(L(t)=a\cos\bigl(b(t-c)\bigr)+1.9\), where \(a\), \(b\) and \(c\) are positive constants.

1. Find the values of \(a\) and \(b\).[4]
2. State the smallest positive value of \(c\).[1]
3. Using this model, find the first time on 7 September 2026 when the tide level is \(1.45\) metres.[4]