Sextant. Correct.
It measures the vertical angle from the horizon (due north, for example) and a celestial body (the north star, Polaris, for example). This angle, combined with the date (day of year for Polaris which does not move, or, the date and the time of day when referencing other bodies such as the sun or moon, which move) gives the sailor what he needs to find his latitude at sea when no land is visible.
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The problem still presents itself to you, for you have not responded to this:
How does the sextant indicate the degrees of latitude north of the equator when you have presumed that the earth is flat?
-- When the sailor is at say the 42nd parallel, he obtains one reading on the sextant, but when he is at the 32nd parallel, he obtains a different reading on the sextant. If he returns to the 42nd parallel, his reading is the same as the first, above, and different from the second, above. Explain why that is the case if the earth is "flat."