"tendre le doigt" or "tendre sa doigt"?

Question

Can you say "elle m'a tendu le doigt" instead of "sa doigt" because you know it's her finger?  I thought when it's obvious to whom the body part belongs, the French prefer not to specify as in "J'ai mal à la tête."

Accepted Answer

oops ignore my error of "sa doigt" I meant "'son doigt" with the same question….thanks. I'm lousy with genders!

Answer

I suspect the use of tendre son doigt has achieved idiomatic status. Note, however, that you still use possessive pronouns when there is special emphasis on the body part. See also: https://french.kwiziq.com/revision/grammar/special-cases-when-you-can-use-mon-ma-mes-etc-with-parts-of-the-body-possessive-adjectives