Final answer:
The latitude of a location where the Sun is 40° above the horizon on December 21, the winter solstice, is approximately 73.5° N. This is calculated by using the altitude of the Sun at noon, knowing that the declination of the Sun is about 23.5° S on this date.
Step-by-step explanation:
On December 21, which is the date of the winter solstice in the Northern Hemisphere, the latitude of a location can be determined based on the altitude of the Sun at noon. If the Sun is 40° above the horizon at noon, we can calculate the latitude by considering that during the winter solstice, the Sun is directly overhead at the Tropic of Capricorn, which is at 23.5° S latitude. Since the altitude of the Sun decreases as we move away from this point towards the equator and then further north, we can find the latitude by subtracting the Sun's altitude from 90° to determine how far away we are from the equator. Then we adjust for the declination, which is the angle between the Sun at the solstice and the celestial equator, to find the exact latitude. In this case, the calculation is as follows: 90° - 40° = 50°. The declination of the Sun is approximately 23.5° S on the winter solstice, so we add this to find out the latitude: 50° + 23.5° = 73.5°. Therefore, the location with the Sun at 40° above the horizon at noon on December 21 would be at a latitude of approximately 73.5° N.