The bad thing about formulae is that you're tossing numbers around, which are meaningless in themselves, especially in the intermediary steps of calculation. There is essentially no error checking there.
With vector analysis, you can do the entire thing in the nav map. By inspection you can determine whether your solution is valid or fallacious. And it takes a tenth of the time of the calculation. Unless it's entirely done by machine math is a poor substitute for vector analysis.
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