ermitteln

You use it when you are in 'problem-solving mode.' In a sentence, the police ermitteln. A scientist might ermitteln a value. At the office, you might ermitteln the cause of a bug. It often takes the preposition wegen (because of/on account of) when talking about crimes. For example: 'The police are investigating because of theft.' It feels official and deliberate.

Use it when you want to sound professional. Use it when discussing news or crime dramas. Use it at work when you are doing a deep dive into data. If you found out who ate your yogurt in the office fridge, you can jokingly say you had to ermitteln. It adds a layer of seriousness to your actions.

Don't use it for casual searching. If you lost your keys, you don't ermitteln. You just suchen (search). Don't use it for 'finding' a restaurant. That is too heavy for a Friday night. It sounds weird if the stakes are too low. Avoid it in very emotional, intimate conversations. It is a head-verb, not a heart-verb.

Germany loves its crime shows, especially 'Tatort.' You will hear ermitteln in almost every episode. Germans value precision and facts. This word reflects that cultural need for a clear result. It comes from the word Mittel (means/way). So, you are literally 'finding the way' to the truth.

The noun form is die Ermittlung. You will see this in news headlines constantly. There is also der Ermittler for a male investigator. For a female, it is die Ermittlerin. If you are just starting an investigation, you might say Ermittlungen aufnehmen. It sounds like you are officially opening a case file.