The seked is a unit of slope and can be expressed as a triangle in which the vertical height is always 1 royal cubit (7 palms) from the convention of the RMP.
For example, a slope with a base of 200 royal cubits and a rise of 100 royal cubits, has a cotangent of 2 which is a dimensionless ratio, but in the convention of the seked evident from RMP this is multiplied by 7 as a reflection of the division of the royal cubit into palms.
Therefore the seked of 14 can be pictured as a simple triangle with a rise of 7 palms (1 royal cubit) and a horizontal run of 14 palms.
It is only the horizontal run that changes so any attempt to represent the slope as a single dimension must be the horizontal run in the context of the seked.
The seked of 14 means nothing without the background knowledge of the unit of length because it is not actually the cotangent.
Desribing it as 'the seked of 14 palms', in which the seked is defined as 'the horizontal run for a fixed vertical rise of 1 royal cubit' seems to me a more convenient definition, if not scientifically correct.
And this is how it is (inadvertently?) described in problem no 56 of RMP on page 48 of Robins and Shute, but later on the same page we read 'the seked is, in fact, exactly 5' for the Bent Pyramid, with no mention of units or that it is the cotangent of 5/7.
But a more scientific definition might be:
'The seked is a ratio which is 7 times the contangent, and it becomes the cotangent on dividing by 7'
Either definition allows us to go back to the triangle with a rise of 1 royal cubit, but the matter can be discussed with fewer words using my definition, or at least that should have been the case if you had accepted that there was no sleight of hand or palm.
These are the steps towards my conclusions:
1. The seked of the Upper Entrance Passage is the width of the passage.
2. The seked of the Ascending Passage is the width of the passage near the junction to the Grand Gallery.
3. The seked of the Upper Entrance Passage is very close to a simple 1 in 2, but different.
4. The seked of the Ascending Passage is close to a simple 1 in 2, but different.
5. The triangle of a simple 1 in 2 slope with an area of 1000 square royal cubits has a slope length of 70.71 royal cubits, a rise equal to the square root 1000 royal cubits, and an area equal to the cotangent x 500.
6. The Ascending Passage has a length of approximately 72 royal cubits, a little longer than 70.71 royal cubits.
7. Draw an analogous triangle with a slope length of 72 royal cubits, and a vertical rise equal to the square root of 1000 royal cubits. (The base of the triangle is 64.68.. royal cubits.)
8. Determine cotangent of said triangle. It is 2.045..
9. Express as a seked (14.31.. palms or 14.31 if you prefer)
10. Draw the triangle with a vertical rise of 1 royal cubit.
11. Calculate the base-length of the triangle in the original unit of length:
2.045.. royal cubits,
14.31.. palms,
57.27 digits to 2 decimal places
Obervation: The circle of the King's Chamber can be viewed in digits, and as a model of the size and shape of the Great Pyramid on a scale of 1 digit to 1 royal cubit, taking pi as 22/7.
Observation: The radian of a circle with a circumference of 360 digits is 57.27 digits to 2 decimal places taking pi as 22/7, or 57 3/11 digits
Conclusions
The slope of the Ascending Passage corresponds to a slope with a vertical rise of 1 royal cubit and a horizontal run of 360/2pi digits, and may have been symbolic of the radian of a circle.
The seked was the unit of slope in ancient Egypt, and a fixed vertical rise of one royal cubit resulted in a simple cotangent, which in this case is 360/56pi with pi taken as 22/7.
There may be a larger circle with a circumference of 360 royal cubits, on a scale of 1 royal cubit to 1 digit, analogous to the ratio of the Pyramid Circle to the King's Chamber Circle.
It is interesting that the bottom of the Entrance Passage corresponds to a level of 360/2pi royal cubits below the level of the Base Square.
Mark