Let the side length of the ascribed square be 1 unit.
tanc = 0.5/1
c = atan(½)°
cos(atan(½)) = a/1
a = 0.894427191 units.
d² = 2(1²)
d= √(2) units.
d is the diagonal of the ascribed square.
e = 45-atan(½)
e = 18.4349488229°
Calculating b.
b² = √(2)²+0.894427191²-2√(2)*0.894427191cos18.4349488229
b = 0.632455532 units.
Therefore,
a/b is;
0.894427191÷0.632455532
= 1.4142135624
= √(2)
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