linguistic:voice_change, structural:expansion, structural:scholar_edition, information:extraction, linguistic:paraphrasing
Angular measurement

Accurate angle measurement has evolved over the years. One simple method is to hold the hand above the horizon with one's arm stretched out. The angular width of the little finger is just over 1.5 degrees at extended arm's length and can be used to estimate the elevation of the Sun from the horizon plane and therefore estimate the time until sunset. The need for more accurate measurements led to the development of a number of increasingly accurate instruments, including the kamal, astrolabe, octant, and sextant. The sextant and octant are most accurate because they measure angles from the horizon, eliminating errors caused by the placement of an instrument's pointers, and because their dual-mirror system cancels relative motions of the instrument, showing a steady view of the object and horizon.

Navigators measure distance on the Earth in degrees, arcminutes, and arcseconds. A nautical mile is defined as 1,852 meters but is also (not accidentally) one arc minute of angle along a meridian on the Earth. Sextants can be read accurately to within 0.1 arcminutes, so the observer's position can be determined within (theoretically) 0.1 nautical miles (185.2 meters, or about 203 yards. Most ocean navigators, measuring from a moving platform under fair conditions, can achieve a practical accuracy of approximately 1.5 nautical miles (2.8 km, enough to navigate safely when out of sight of land or other hazards.