Let BD = CD = 1 unit.
a = 180-45-30
a = 105°
a is angle CAD.
(1/sin105) = (b/sin45)
b = 0.73205080757 units.
b is AC.
c² = 0.73205080757²+2²-2*2*0.73205080757cos30
c = 1.41421356237 units.
c is AB.
( 1.41421356237/sin30) = (2/sind)
d = 45°
e = 180-d
e = 180-45
e = 135°
e is angle BAC.
Therefore, the required angle alpha is, let it be f.
f = e-a
f = 135-105
f = 30°
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