Calculating BD/AC.
Let 1 unit be AB = AD.
a = 180-30-30
a = 120°
a is angle BAD.
b² = 2-2cos120
b = √(2-2cos120)
b = √(3) units.
b is length BD.
c = 180-15-45
c = 120°
c is angle BCD.
(√(3)/sin120) = (d/sin45)
d = √(2) units.
d is length BC.
e² = 1²+√(2)²-2*√(2)*1cos(30+15)
e² = 3-2
e = √(1)
e = 1 unit.
e is length AC.
It implies;
Length BD÷Length AC is;
√(3)÷1
= √(3)
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