Sun's Altitudes at Time of Late Afternoon Prayer for Any Latitude

For instance, the Sun's declination on February 2 is -16.48º in Istanbul; hence, ghâyat irtifa' (point of solar culmination, the Sun's maximum altitude) is -16.48º + 49º = 32.12º; fay-i-zawâl (the shortest shadow) of a one-metre-long perpendicular rod is 1.58m.; and the length of its late-afternoon shadow is 2.58m.; and the Sun's late-afternoon altitude is 21.20º. The fadl-i-dâir (temporal value of the arc of complement of the Sun's true altitude) is 2 hours  and 41 minutes, which will be found by using a calculator. Thereby the time of late afternon will be found to be 9.42 hours, adhâni, and 3.09 hours, in standard time, since the equation of time is -13.39; (Please click here to see Table Equation of Time and Declination of The Sun) A method to be used in the absence of the chart above is to get a privileg calculator, touch the buttons for the computation: 90 - 32.12  = tan + 1 = arc tan MS 90 - MR = , and find the Sun's altitude at the time of 'asr-i awwal (the earlier time of late afternoon) to be 21.08º. There is yet another method: The Rub-i-dâira (quadrant). Its khayt, (thread that represents the daily rotation,) is brought over the number representing the ghâyat irtifâ'; the number on the arc of zill-i-mebsût and crossed by the khayt shows the length of the shortest shadow termed fay-i-zawâl.