the way

[VicNicSor]

She was surprised at the way her footsteps plodded down the path of their own volition.
The Pastures of Heaven by John Steinbeck

I ... I too had had a transaction with him during that month, but on this occasion I was rather surprised at the way he came in.
A Raw Youth by Fyodor Dostoevsky

blow up
to become very angry with someone:
I was surprised at the way he blew up at Hardy.
Longman dictionary

"The way" here means:
... the manner in which
... the very fact that (I think it's this)

Thanks.

 

[Parla]

You're right that it could mean either. All three are ambiguous, but I think the first two are more likely "the way in which", while the third is more likely "the very fact that".

 

[Packard]

I was surprised at the way he blew up at Hardy.
Longman dictionary

"The way" here means:
... the manner in which
... the very fact that (I think it's this)

I think you could interpret it either way. But rather than "the very fact" I would use "under the circumstances".

 

[Myridon]

I could be surprised that he blew up at all or I could be surprised that he threw something at Hardy rather than just yelling.

 

[JordyBro]

All of these are "the manner in which". If anyone wanted something to mean "the fact that", they would say, "the fact that".

 

[suzi br]

All of these are "the manner in which". If anyone wanted something to mean "the fact that", they would say, "the fact that".

I do not see how you can be so certain about matters of style. "The very fact that" is part of the definition quoted in #3 and seems the most reasonable way to read the first sentence in the OP, since the girl's feet are moving by their own volition, a fact that surprises the girl

 

[VicNicSor]

The Russian translation of 1) really gives it as She was surprised that her footsteps.
The original of 2) sounds like " I was rather surprised that he came in.", too. Though, reading some context, the character in question, entering room, really behaved unusually.

That's why I tended to think they're about a "fact".

Thanks to everyone.