In order for this question to 'make sense' some assumptions must be made.
The North Star is not 'exactly' positioned on the North Celestial Pole but is offset by about 42'. Therefore as the world turns it is only 'exactly' at 90 degrees North with respect to the horison twice a day at different times of the day throughout the year, as the Earth rotates and revolves around the Sun. Since the day or time is not specified the precise alignment of the North Star with the horison at various times of the day and year might be off by as much as 42'.
Assuming the North Star is at the time measured, precisely horisontal to true north, the angle between it and the horison would be the same as ones latitude given a perfectly spherical uniform globe with no atmospheric aberrations.
Neither is the rate of the Sun's progress across the sky entirely constant. The Earth�s orbit being somewhat elliptical its time of rotation with respect to the Sun varies throughout the year. However, within the ~30 minute time frame specified here the deviation would be virtually insignificant. Relativistic effects over this brief period of time would also be of little consequence. In combination the calculated location could be off by perhaps an inch or so.
Taking this simplified view, the angle of the North Star above the horison is synonymous with ones
latitude, 46�, 23' (46.38333�).
Similarly the Earth�s rotation beneath the Sun is ~360� in 24 hours (15�/hr. = 1�/4min.) or ~
7.63325� (7�, 38�) longitude east in 30.533 minutes.
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