The phrase "acknowledged a third" is correct and usable in written English.
It can be used in contexts where someone recognizes or accepts the existence or contribution of a third party or element in a discussion or situation.
Example: "During the meeting, she acknowledged a third party's role in the project's success."
Alternatives: "recognized a third" or "accepted a third."
"We suspect that something like this is happening," Dr. Campins said, but acknowledged a third possibility: The asteroids could contain enough radioactive isotopes to melt ice deep below the surface, creating liquid water that seeps upward before vaporizing.
In addition to the usual demarcation between black and white, since the 1700s New Orleans had acknowledged a third class, free people of colour (in French, gens de couleur libres), sometimes called Creoles, the freed descendants of European fathers and African mothers who had enjoyed a great deal of autonomy.
He has, as a conservative critic acknowledged, "a first-class intellect and a first-class temperament".
It is interesting to note in this connection both the OED's aforementioned sense of 'forgivable' as a condition which merits forgiveness, as well as Butler's typology of anger which acknowledges a third type that includes such stable postures as irritability, sullenness, or churlishness, which link anger more to relatively fixed character traits than to instincts, cognitions, or actions.
While our selective memory owes debts to the allure of the Olympics and a tendency to privilege familiar political struggles, we must also acknowledge a third important factor.
And while it's not untrue to say that these three legends, who broke such fertile ground in portraying the struggle of the alienated Everyman, made me want to be a writer, I would be remiss if I didn't acknowledge a fourth artistic influence, one who might not come so readily to mind when thinking of literary inspiration but who is equally important to me: the radio host Howard Stern.
On the one hand, he acknowledged, a show whose first act concludes with its entire cast singing Whitesnake's "Here I Go Again" would seem to have different ambitions from, say, "West Side Story".
Reichelt said he acknowledged about a third of staff were unhappy with the Abbot Point decision.
What I found most revolutionary and inspiring is how this otherwise marginalized community of roughly 2 million people in India took their demand to be acknowledged as a third gender all the way to the Supreme Court.
It is best to draw a discreet veil over England's second-half performance other than to acknowledge a memorable second try for Slater who galloped 90 metres having been set free by Inglis.
