NavList:

Brian Walton, you wrote:
"11 and a quarter degrees. 11.25°. Try that in decimals"

FR: You just did! 11.25° is decimal degrees. I think you have confused the use of "radians" or pure angles with decimal angles or the metric system or something like that. Using decimal degrees has some significant advantages over sexagesimal degrees, minutes, and seconds. 

Isn’t it just horses for courses? Steering a sailing vessel, you’re concerned with horizontal angles.  You start with North, East, South, and West, i.e quarters, and start splitting the angles in two until you get to 64ths, i.e ½  points, i.e 5&5/8 degrees, which is the closest it was felt it was possible  to steer with the compasses, vessels, and helmsmen of the time.  OK, a ¼ point if you’re a perfectionist.
With celestial, you’re measuring vertical angles and you both can and need to do better than that.  By the 16^th century, chaps like Tycho Brahe were using degrees.  I’m unclear if they divided the interval between into minutes or decimals of a degree, probably the latter if they were using scale lines on giant quadrants.  DaveP