"By how" or "By the way" in this case?

Question

By how (or 'the way') he reacted to the question, it was clear he was hiding something.

Both 'how' and 'the way' have the same meaning in this context. Like when we say:

I like the way (or 'how') she dances.

However, in the first case, it strikes me as odd, probably because we can start a sentence with 'By the way' to mean 'Incidentally'. So, my question is, do you recommend I should use 'how' to avoid misunderstanding, or is it clear from the context?

Answer 1

Both "how" and "the way (that)" are perfectly acceptable in either sentence. I disagree with the comment saying that "how" is less formal; to me, they seem equivalent.