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I have now looked up the result in a book. The opening
angle of the wavelet fronts is 109.5 degrees, independent
of boat velocity. The book, "Bores, Breakers, Waves, and
Wakes" by R. A. R. Tricker, first published in 1964 by
Mills & Boon Limited, London, has a very clear derivation
which should be quite accessible to brighter IB students.
The downside is that the book itself is not very
accessible. I couldn't find it at six booksellers' web
sites that I tried.