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Additional precision can be provided using decimal fractions of an arcsecond. Maritime charts are marked in degrees and decimal minutes to facilitate measurement; 1 minute of latitude is 1 nautical mile. The example above would be given as 40° 11.25′ (commonly written as 11′25 or 11′.25). [13]
The values of sine and cosine of 30 and 60 degrees are derived by analysis of the equilateral triangle. In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained.
Decimal degrees (DD) is a notation for expressing latitude and longitude geographic coordinates as decimal fractions of a degree. DD are used in many geographic information systems (GIS), web mapping applications such as OpenStreetMap, and GPS devices. Decimal degrees are an alternative to using degrees-minutes-seconds notation. As with ...
Whether they are converted to decimal degrees or radians depends upon the particular calculating machine or program. Angles in the hours ( h), minutes ( m), and seconds ( s) of time measure must be converted to decimal degrees or radians before calculations are performed. (1 h = 15° 1 m = 15' 1 s = 15")
The second of arc (or arcsecond, or just second) is 1 / 60 of a minute of arc and 1 / 3600 of a degree (n = 1,296,000). It is denoted by a double prime ( ″ ). For example, 3° 7′ 30″ is equal to 3 + 7 / 60 + 30 / 3600 degrees, or 3.125 degrees. The arcsecond is the angle used to measure a parsec: grad
degrees and decimal minutes: 40° 26.767′ N 79° 58.933′ W; decimal degrees: +40.446 -79.982; There are 60 minutes in a degree and 60 seconds in a minute. Therefore, to convert from a degrees minutes seconds format to a decimal degrees format, one may use the formula
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Degrees given to three decimal places ( 1 / 1000 of a degree) have about 1 / 4 the precision of degrees-minutes-seconds ( 1 / 3600 of a degree) and specify locations within about 120 metres (390 feet).