Final answer:
On December 21st at 76.1 degrees south latitude, the zenith angle for the Sun is 52.6 degrees because the Sun is directly over the Tropic of Capricorn,
Step-by-step explanation:
The zenith angle for a person standing at 76.1 degrees south latitude on December 21st, the date of the winter solstice in the Northern Hemisphere, can be determined by considering the position of the Sun in relation to Earth's latitudes on that day.
Since the Sun is at the zenith at the Tropic of Capricorn (23.5 degrees south latitude) on December 21st, we can calculate how far the Sun is from the zenith at 76.1 degrees south latitude.
To find the zenith angle, subtract the latitude of the Tropic of Capricorn from the latitude of the observer: 76.1 degrees - 23.5 degrees = 52.6 degrees.
Now, because the Sun is at the zenith at the Tropic of Capricorn, it will be 52.6 degrees away from the zenith for someone at 76.1 degrees south latitude. Therefore, the zenith angle is 52.6 degrees.