At the winter solstice for the northern hemisphere, the Sun is over the Tropic of Capricorn at 23 degrees 26 minutes south. Your observer is at 38N, a difference in zenith angle of 38+23.5=61.5 degrees. The elevation of the Sun above the southern horizon at noon (more precisely "Local Apparent Noon") is 90 - the azimuth angle, or 28.5 degrees.
Noon by your clock probably isn't "local apparent noon", the time when the Sun is in transit - at its highest point in the sky. For example, I live near Sacramento, CA, and here, in daylight savings time, the Sun transited my longitude at 12:57PM today. If I were a sailor (which I used to be) I could take a single "noon sight" of the Sun and calculate my position quite accurately with a single observation.
I need to watch the Sun through my sextant, and take continuous readings of the elevation angle of the Sun. (On the deck of a pitching boat, this observation can be tricky!) I note the time when the Sun is no longer rising in the sky, and starts to set; that time, to the nearest 15 seconds, gives me my longitude. The elevation angle at that time tells me my latitude. I do need to have an accurate watch, and a copy of the Nautical Almanac, but every modern sailor has these things.
Back in 1714, the British Admiralty offered a prize of twenty thousand pounds - a king's ransom, back then! - for the invention of a clock that kept accurate time at sea, because your celestial position is only as accurate as your clock!
The winter solstice (shortest day) of the northern hemisphere is simultaneously the longest day (the summer solstice) in the southern hemisphere. The southern hemisphere summer solstice, falls between December 20 and December 23 inclusive.
That may happen - at different times of the year - in any latitude between the tropics - that is, between 23.5 degrees north, and 23.5 degrees south. Note that this angle is precisely the tilt of Earth's axis.
The northern and southern Hemispheres each consist of a range of 90 degrees of latitude. They meet at the equator ... it's the boundary between them. There's no gap between them at the equator, so if you wanted to, you could go to the equator and stand with one foot in each hemisphere. Each hemisphere is shaped like ... like ... like a hemisphere. That's like half of a grapefruit. Their edges fit together to make a complete sphere, and the distance between them at their edges, as well as the angle between them, is zero.
The sun will be directly overhead at noon for locations along the Tropic of Cancer (23.5 degrees north latitude) on the June solstice and locations along the Tropic of Capricorn (23.5 degrees south latitude) on the December solstice. In between those latitudes, the sun will be high in the sky but not directly overhead at noon.
The angle of the Sun in the sky, its maximum height above the horizon, depends on a measurement called its declination, which varies over a range of ±23.5 degrees. The Sun's declination is zero at the equinoxes, and is +23.5 degrees at the summer solstice (in the northern hemisphere), the longest day, and -23.5 degrees at the winter solstice, the shortest day. Declination is the Sun's latitude on the celestial sphere, and the declination of any obect is equal to the latitude of a set of points along a line of latitude on the Earth's surface at which it passes overhead.
Latitude is zero at every point on the equator.
The angle between the Pole Star and the horizon is equal to your latitude.
The winter solstice (shortest day) of the northern hemisphere is simultaneously the longest day (the summer solstice) in the southern hemisphere. The southern hemisphere summer solstice, falls between December 20 and December 23 inclusive.
It can be anything from zero hours to 24 hours, depending on where on Earth you are, and whether you are talking about the summer solstice or the winter solstice. At the summer solstice, the day is between 12-24 hours, depending on your location, and the night is between 0 and 12 hours.
The time between sunrise and sunset is a little longer each day from the December solstice to the June solstice in the northern hemisphere and from the June solstice to the December solstice in the southern hemisphere.
At the time of the southern hemisphere's winter solstice, the sun is directly over the Tropic of Cancer, which circles Earth at 23.44° north latitude. So at 6° south latitude the sun appears 29.44° from the zenith (a location's zenith is directly overhead). Since there are 90° between the zenith and the horizon, the angle for which you are looking is the difference between 90° and 29.44°, 60.56°.
Washington is farther from the equator than California. The closer you get to the equator, the less the amount of daylight per day deviates from 12 hours. The closer you get to the poles, the greater the difference in the amount of daylight between the summer solstice and the winter solstice. I used to live between 40° and 41° north latitude. The amount of daylight there on the summer solstice is about 15 hours, and it's about 9 hours on the winter solstice. Now I live near 30° north latitude, where we get about 14 hours of daylight on the summer solstice and about 10 hours on the winter solstice.
The northern pole star "Polaris" is visible in the sky to an observer located anywhere on earth between the equator and the north pole, i.e. anywhere with a north latitude. There is no similar southern pole star.
In the Northern Hemisphere the summer solstice will usually happen between June 20 and June 22. For the Southern Hemisphere it will occur between December 20 and December 23.
The summer solstice starts between June 20th and 21st in the northern hemisphere, and between December 21st and 22nd in the southern hemisphere.
The 42nd parallel forms the southern boundary of Idaho. It marks the border between Idaho and Nevada as well as a portion of the border between Idaho and Oregon.
Trade winds blow from the northeast in the Northern Hemisphere and from the southeast in the Southern Hemisphere. In the Northern Hemisphere, they are typically found between 30 and 60 degrees latitude, while in the Southern Hemisphere, they occur between 0 and 30 degrees latitude.