capable
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capable of
Having the competence, talent, or possibility to do something specific. Usually in the construction 'fähig sein zu etwas' (to be capable of something).
Nach dem Intensivkurs ist sie fähig, ein Gespräch auf Spanisch zu führen.
After the intensive course, she is capable of holding a conversation in Spanish.
The adjective 'fähig' (capable) is closely related to the noun 'die Fähigkeit' (the ability). If a person is capable of doing something, then they have the ability to do it.
Er hat die Fähigkeit, komplexe Probleme schnell zu verstehen.
He has the ability to understand complex problems quickly.
The adjective 'fähig' (capable) is very often used with the preposition 'zu' and the dative. To describe an activity, you use the structure 'fähig sein, etwas zu tun' (to be capable of doing something) or 'zu etwas fähig sein' (to be capable of something).
Er ist zu unglaublichen Leistungen fähig.
He is capable of incredible achievements.
When 'fähig' (capable) stands directly before a noun, it describes a person as generally competent in their profession or role. It is then used without the preposition 'zu'.
Wir suchen eine fähige Mitarbeiterin für unser Team.
We are looking for a capable employee for our team.
situation / location
'in der Lage sein' and 'fähig sein' can both express that someone can do something. 'in der Lage sein' often emphasizes the possibility in a specific situation: you have enough time, strength, or means. 'fähig' more strongly describes a person's ability, competence, or quality. So you can be capable of solving a task, but not be in a position to do it right now because you are ill or have no time. The risk of confusion lies in the fact that both are related to 'können' (can / be able to).
Sofia ist fähig, das Team in schwierigen Momenten ruhig zu führen.
Sofia is capable of leading the team calmly in difficult moments.
Nach der langen Reise bin ich nicht in der Lage, sofort weiterzuarbeiten.
After the long trip, I am not able to continue working right away.