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The paper explains how the ancient Egyptian architects used the arithmetic of unit-fractions to reckon the astronomical tilt of 26° 31' 23" ±5" for the Great Pyramid’s entrance passage, which is correlated to the latitude of ~ 29° 58' 45" north and Earth’s axial tilt ~24° 6' of nearly 5070 years ago. Therefore, in the beginning, the paper explains for the first time, with the supporting translation, the architectonic and geometric reckoning methods of almost 40% of the so-called Rhind Mathematical Papyrus (RMP). Firstly, it explains the meanings of 36 mathematical and geometric symbols in RMP’s hieratic text. Secondly, in relation to the divisions of the Egyptian cubit rod, it explains the architectonic decomposition method of the 2/n table on decomposing the sum of two unit-fractions, such as 1/n, into other unit fractions, where n is an odd number from 3 to 101. It shows that this recto table, which represents almost 1/3 of RMP, is on subdividing line-segments like 2/n into only measurable parts. Thirdly, it shows that RMP#24 is an example of calculations related to the sine of an angle and RMP#74 is an example of calculating the values of angles. Fourthly, it shows that RMP#65 is an example of using a grid-system to plot and subdivide the arc of half the side of an octagon into 10 parts. Finally, the paper shows how the pyramids designers used these ancient Egyptian mathematical and geometric methods in reckoning and implementing the astronomical tilt of the Great Pyramid’s entrance passage in the Giza Plateau. [ABSTRACT FROM AUTHOR]