A sagacious person understands a situation and judges it well — not only book-smart, but sharp about people, choices, and what is likely to happen. You might call a leader sagacious, or a grandmother, or a quiet remark that turns out to be right. It is a high, bookish word. You will meet it in novels and speeches far more than at the night market. Though actually, sagacious is stronger than clever. Clever can be quick and a bit showy; sagacious is deep, patient, and trusted. When someone says “how sagacious” with a smile, they may be teasing, because the word sounds so grand. Formal English. A kind teacher in real talk would just say wise, or “she reads people well.”