Translation of "D'acquiescer" in English

C'est plus facile d'acquiescer en hochant la tête quand elle est vide.

It's easier to nod when your head is empty.

J'ai expliqué la situation en long, en large et en travers, mais ils se sont contentés d'acquiescer sans montrer plus d'intérêt que ça.

I explained the situation, as this, that and such and such, but they just nodded along without showing much interest.