
die Wut
anger
A very strong, intense feeling of anger and outrage.
Er war so voller Wut, dass er zitterte.
He was so full of anger that he was shaking.
anger
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anger
A very strong, intense feeling of anger and outrage.
Er war so voller Wut, dass er zitterte.
He was so full of anger that he was shaking.

to take one's anger out on someone
To direct one's anger at a person who is often not the actual reason for the anger.
Nur weil du einen schlechten Tag hattest, musst du deine Wut nicht an mir auslassen.
Just because you had a bad day, you don't have to take your anger out on me.
The noun 'die Wut' (anger) describes the feeling, while the adjective 'wütend' (angry) describes the person who has this feeling. Both words have the same stem.
Er war so wütend, dass seine Wut kaum zu kontrollieren war.
He was so angry that his anger was barely controllable.
To express whom or what you are angry at, use the preposition 'auf' followed by the accusative. Alternatively, you can also use 'Wut über + accusative' (anger about/over).
Sie hatte eine riesige Wut auf ihren Chef.
She had enormous anger toward her boss.
'Wut' (anger) is often combined with vivid expressions to show the strength of the feeling. Typical phrases are 'vor Wut kochen' (to be boiling with anger), 'Wut im Bauch haben' (to have anger in one's belly), or 'blind vor Wut sein' (to be blind with rage).
Als er die Nachricht hörte, kochte er vor Wut.
When he heard the news, he was boiling with anger.
In the idiom 'seine Wut an jemandem auslassen' (to take one's anger out on someone), the structure is fixed. The person who is the target of the anger is always in the dative.
Bitte lass deine Wut nicht an mir aus!
Please don't take your anger out on me!
annoyance / trouble
Ärger and Wut are negative feelings, but they differ in intensity. Ärger refers to general annoyance and can be considerably less intense. Wut is appropriate when the feeling is very strong and fierce.

Die erneute Zugabsage ohne jede Information löste bei Nora große Wut aus.
The train being canceled again without any information made Nora extremely angry.
Die zehnminütige Zugverspätung löste bei Nora Ärger aus.
The ten-minute train delay annoyed Nora.