Determine the ALTITUDE and DIRECTION (What direction would you have to face in order to see the sun)?

Question

Here is the Problem

1.- October Revolution Island, Russia (79 degrees N, 98 Degrees E)
(Get ALTITUDE and DIRECTION for each date)
March 21
June 21
September 21
December 21

2.- Chaochow, China (23.5 degrees N, 117 degrees E)

March 21
June 21
September 21
Decmeber 21

3.-Macapa, Brazil (Lat.= 0 degrees, 51.5 degrees W)

March 21
June 21
September 21
December 21

4.- Dunedin, New Zealand (Lat.= 46 degreees S, Long= 170 degrees E)

March 21
June 21
September 21
December 21


(Please tell which answer is for which date and problem, and please explain me how you obtained it) Thanks for your help

Answer 1

The answer depends on the time of day but I'm guessing the problem wants you to assume it is when the sun is at meridian (solar noon).

Each date given is either an equinox or solstice.
March = northward equinox
June = northern solistice
September = southward equinox
December = southern solstice

At the equinoxes, the altitude of the sun is equal to your co-lattitude. Your colattitude is 90 - lattitude. So, for the russian island, the co-lattitude is 90 - 79 = 11. At the equinox, the sun would be 11 degrees in altitude.

At the solstices, the altitude is the co-lattitude plus or minus 23.5 degrees, depending on the equinox and the hemisphere you're in. Northern hemisphere northern solstice is + 23.5 degrees, norther hem, southern solstice is - 23.5 degrees. Same basic relationship for the south. If you get a negative number, the sun is below the horizon. If you get a number bigger than 90, subtract it from 180, and flip the direction you look at.

So here we go
1)
March: 90-79 = 11, South
June: 90-79+23.5 = 34.5, South
September: 90-79 = 11, South
December: 90-79-23.5 = -12.5, South (below horizon)

2)
66.5, South
90, straight up
66.5, South
43, South

3)
90, straight up
66.5, North
90, straight up
66.5, South

4)
44, North
20.5, North
44, North
67.5, North