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

Ghâyat
Irtifa'
Fay-i-
zawâl
Ghâyat
Irtifa'
Fay-i-
zawâl
Ghâyat
Irtifa'
Fay-i-
zawâl
Ghâyat
Irtifa'
Fay-i-
zawâl
Ghâyat
Irtifa'
Fay-i-
zawâl
0.15 229.182 10.30 5.395 25.30 2.097 40.30 1.171 61 0.554
0.30 114.589 11.00 5.145 26.00 2.050 41.00 1.150 62 0.532
0.45 76.390 11.30 4.915 26.30 2.006 41.30 1.130 63 0.510
1.00 57.290 12.00 4.705 27.00 1.963 42.00 1.111 64 0.488
1.15 45.829 12.30 4.511 27.30 1.921 42.30 1.091 65 0.466
1.30 38.188 13.00 4.331 28.00 1.881 43.00 1.072 66 0.445
1.45 32.730 13.30 4.165 28.30 1.842 43.30 1.054 67 0.424
2.00 28.636 14.00 4.011 29.00 1.804 44.00 1.036 68 0.404
2.15 25.452 14.30 3.867 29.30 1.767 44.30 1.018 69 0.384
2.30 22.904 15.00 3.732 30.00 1.732 45.00 1.000 70 0.364
2.45 20.819 15.30 3.606 30.30 1.698 45.30 0.983 71 0.344
3.00 19.081 16.00 3.487 31.00 1.664 46.00 0.966 72 0.325
3.15 17.611 16.30 3.376 31.30 1.632 46.30 0.949 73 0.306
3.30 16.350 17.00 3.271 32.00 1.600 47.00 0.933 74 0.287
3.45 15.257 17.30 3.172 32.30 1.570 47.30 0.916 75 0.268
4.00 14.301 18.00 3.078 33.00 1.540 48.00 0.900 76 0.249
4.15 13.457 18.30 2.989 33.30 1.511 48.30 0.885 77 0.230
4.30 12.706 19.00 2.904 34.00 1.483 49.00 0.869 78 0.213
4.45 12.035 19.30 2.824 34.30 1.455 49.30 0.854 79 0.194
5.00 11.430 20.00 2.747 35.00 1.428 50.00 0.839 80 0.179
5.30 10.385 20.30 2.675 35.30 1.402 51.00 0.830 81 0.158
6.00 9.514 21.00 2.605 36.00 1.376 52.00 0.781 82 0.141
6.30 8.777 21.30 2.539 36.30 1.351 53.00 0.754 83 0.123
7.00 8.144 22.00 2.475 37.00 1.327 54.00 0.727 84 0.105
7.30 7.596 22.30 2.414 37.30 1.303 55.00 0.700 85 0.087
8.00 7.115 23.00 2.356 38.00 1.280 56.00 0.675 86 0.070
8.30 6.691 23.30 2.300 38.30 1.257 57.00 0.649 87 0.052
9.00 6.394 24.00 2.246 39.00 1.235 58.00 0.625 88 0.035
9.30 5.976 24.30 2.194 39.30 1.213 59.00 0.601 89 0.017
10.00 5.671 25.00 2.145 40.00 1.192 60.00 0.577 90 0.000

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.