Troy has a container in the shape of a rectangular prism with a \(40\text{ cm}\) by \(60\text{ cm}\) base and a height of \(30\text{ cm}\). He labels the vertices of a \(40\text{ cm}\) by \(30\text{ cm}\) side face \(A\), \(B\), \(C\), and \(D\), with \(A\) and \(B\) being vertices of the base face too. He then puts some water in the container and tilts the container along \(AB\) until the water completely covers face \(ABCD\). (He is able to do this so that no water is lost!) At this point, the water still covers \(\frac{4}{5}\) of the base area.
Determine the depth of the water, in centimetres, when the container is level.