I came across this sentence:
He wrinkled his nose in disgust at the smell.
I wonder why not:
He wrinkled his nose in disgust of the smell.
Does it make any difference why we don't use of?
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I am not sure there is an answer to why we use at instead of of that is substantially better than "Because that is the way English is." I am sure your native language also has cases where you use one preposition and not another.
But we often use at to mean "caused by" in the case of reactions, or to mean "on the occasion of".