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Originally Posted by Rockin Robbins
It's nice to understand the underlying math. It's stupid to actually use it to perform an attack.
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Certainly the Fast-90 method is an excellent technique and is useful in many situations. With all due respect, however, real U-boat commanders would not have thought it stupid to use trigonometry to achieve a favorable attack position and generate a firing solution. In fact, they had tools to help with exactly that. The most obvious and advanced was, as you mentioned, the TDC or Torpedovorhaltrechner .
There is also evidence that they had available and used trigonometry tables to calculate precise lead angles for intercepting and firing on targets. For example, the instruction manual for the Angriffsscheibe 2 mit Kompaßscheibe (attack disc) mentions that the lead angle is taken from a table ("Vorhalt ... Tabelle") which is undoubtedly a trignometry table relating to the law of sines. While they would not need to use these tools for every attack, they would be well-trained and ready to do so (such as in the case of a damaged TDC, see U.Kdt.Hdb. Part 145).
While rules of thumb are useful (especially for desperation shots), a good U-boat commander would be prepared to use a variety of techniques to generate precise and accurate firing solutions so as not to waste a single precious torpedo (see U.Kdt.Hdb. Parts 91, 105).