Normal mean and standard deviation from an upper-tail probability and a conditional probability

The length of a fish in a large lake follows a normal distribution, with mean \(\mu\text{ cm}\) and standard deviation \(\sigma\text{ cm}\).

Of all the fish in the lake, \(30\%\) are longer than \(42\text{ cm}\).

Of the fish that are longer than \(42\text{ cm}\), \(20\%\) are longer than \(47\text{ cm}\).

Find \(\mu\) and \(\sigma\).[7]