How many arcseconds are in a degree?

1 Answer
Apr 25, 2018

There are 3600 arcseconds in 1 degree.

Explanation:

We can use dimensional analysis to convert from degrees to arcminutes, then from arcminutes to arcseconds:

color(white)=1^@

=1^@*"60 arcminutes"/1^@

=color(red)cancelcolor(black)(1^@)*"60 arcminutes"/color(red)cancelcolor(black)(1^@)

="60 arcminutes"color(white)*

="60 arcminutes"*"60 arcseconds"/"1 arcminute"

="60"color(red)cancelcolor(black)"arcminutes"*"60 arcseconds"/("1"color(red)cancelcolor(black)"arcminute")

=60*"60 arcseconds"/1

=60*"60 arcseconds"

="3600 arcseconds"color(white)*