For any two longitude lines (meridians), east-west distance between them
is at maximum at the Equator. It diminishes with increasing (northward) or
decreasing (southward) latitude toward zero (at the poles).
3° W places the point along the center line of zone 30, and hence on
a meridian. Along the meridian, 22°30' N places the point at 22 * 60
+ 30 minutes north of the equator and so at 22 * 60 + 30 nautical
miles north of the equator which is approximately 1350 * 1.154 * 1.61
kilometers north i.e. approximately 2508 kilometers north.
So the UTM coordinates, in kilometers, are 30 500
2508N
Again, 3° E places the point along the center line of the UTM zone,
now zone 31. And the northing distance is the same, but in the
opposite direction. For points in the Southern Hemisphere, the Equator
has northing component 10,000,000 (in meters) and so the northing
coordinate of our point is 10,000 - 2508 (in kilometers) or the
equivalent in meters.
So the UTM coordinates, in kilometers, are 31 500
7492S
122°20' is between 128° and 120° so the point is in UTM zone 10, 2°20'
from the eastern boundary or, equivalently, 40' east of the center
line. Then the easting component is 500,000 + 40 * 1.154 * 1.61 or,
approximately, 574 (in kilometers). 0° N places the point on the
Equator.
So the UTM components are 10 574 0N
UTM zone 5 is between (180 - 24)°W and (180 - 30)°W longitude, i.e.
between 156°W and 150°W. Easting component 500 places the point on
the center line of the UTM zone, i.e. at 153°W longitude. Northing
component 5000 places the point 5000 km. north of the Equator. To
convert to degrees and minutes, change first to nautical miles. 5000
km. --> 5000/1.61/1.154 nautical miles --> approximately 2691
nautical degrees, which is equvalent to 2691 minutes along a meridian.
2691 = 44 * 60 + 51 minutes.
So the point is at 44°51'N 153°W
UTM zone 20 is between 26° and 20°W longitude. Easting component 500
places the point on the centerline of the UTM zone. So the longitude
component is 23°W. Along the meridian, the northing component 2750S
places the point at 10,000 - 2750 kilometers south of the Equator.
Converting to nautical miles 10,000 - 2750 kilometers -->
7250/1.61/1.154 --> approximately 3902 nautical miles. 3902 = 65 *
60 + 2, so the point is at 65°2'S latitude.
The lat-lon coordinates are 65°2'S 23°W.
UTM zone 60 is between 174° E and 180°E longitude. So the point is
on the equator 100 kilometers east of the center of the zone, i.e.
east of 177°E. Converting to DMS, 100 kilometers --> 100'1.61/1.54
nautical miles --> approximately 54 minutes.
So the lat-lon coordinates are 0°N 177°54'E