Final answer:
The sextant is the navigational instrument that uses double reflection to measure angles between two objects, essential for maritime navigation to determine latitude. Older instruments like the cross-staff and backstaff also served similar functions, while the astrolabe helped mariners using the stars or the Sun for latitude determination.
Step-by-step explanation:
The mapmaking and navigational instrument that measures the angle between two objects using double reflection is known as the sextant. It comprises an arc that represents 1/6 of a circle, which is reflective of its name. By utilizing a pivoted mirror, the sextant allows the user to view two objects at once and measure the angle between them. This tool was and is crucial for navigation, especially at sea, for determining one's latitude by measuring the elevation of celestial bodies such as the Sun above the horizon.
Historically, other tools like the cross-staff and the backstaff were also used for similar purposes. The cross-staff allowed scholars to measure the elevation angle of the noontime Sun, and mariners later transitioned to the backstaff to avoid the dazzling sun on their eyes. The surveyor's telescope or theodolite is another related instrument that measures angles but is more commonly used in surveying rather than navigation.
Astrolabes were another ancient instrument used for navigation, measuring the altitude of stars or the Sun, and helping sailors to determine their latitude while at sea. While astrolabes and sextants serve a similar function in navigation, their designs and historical periods of prominent use differ.