On the shortest day of the year in Fairbanks, Alaska, it looks like this. Some data from
Wolfram Alpha: Sunrise: 10:59 am. Sunset: 2:41 pm. Length of day: 3 hours 42 minutes. Height of the sun at local noon (12:50 pm): 1.729 degrees. Diameter of the sun: 0.5 degrees. It was cloudy, so we couldn't see it anyway.