Calculation of a Shadow Square

Spread Sheet (Excel) Formulae and Table of Angles

Distance to Object (Umbra Versa) Height of Object (Umbra Recta) Angle, Radians Angle, Degrees
 A B =ATAN2(A,B) =C*180/PI()
12 1 0.0831412318884412 4.77
12 2 0.165148677414627 9.46
12 3 0.244978663126864 14.04
12 4 0.321750554396642 18.43
12 5 0.394791119699762 22.62
12 6 0.463647609000806 26.57
12 7 0.52807444842636 30.26
12 8 0.588002603547568 33.69
12 9 0.643501108793284 36.89
12 10 0.694738276196703 39.81
12 11 0.741947268005917 42.51
12 12 0.785398163397448 45
11 12 0.828849058788979 47.50
10 12 0.876058050598194 50.19
9 12 0.927295218001612 53.13
8 12 0.982793723247329 56.31
7 12 1.04272187836854 59.74
6 12 1.10714871779409 63.43
5 12 1.17600520709514 67.38
4 12 1.24904577239825 71.57
3 12 1.32581766366803 75.96
2 12 1.40564764938027 80.54
1 12 1.48765509490646 85.24

Note that in column C, the Angle in Radians, I am using ATAN2, which in Excel is the arctangent of x & y coordinates, where x = number in column A and y = number in column B. Column D then converts the angle into degrees, since there are 2 pi radians in a circle (pi radians = 180°).