Mathematics Question and Solution
Let CE = 1 unit.
(1/sin20) = (a/sin40)
a = 1.87938524157 units.
Where a is AE.
Notice;
b = a-1
b = 1.87938524157-1
b = 0.87938524157 units.
Where b is AD.
Angle AEC = 180-20+40
Angle AEC = 120°
(c/sin120) = (1/sin20)
c = 2.53208888624 units.
Where c is AC = BC.
BE = 2.53208888624-1
BE = 1.53208888624 units.
Angle BED = 180-120 = 60°
(BD)² = 1.53208888624²+1-2*2.53208888624cos60
BD = 1.34729635534 units.
Calculating Angle BDE (alpha, the required angle).
Let it be d.
(1.53208888624/sind) = (1.34729635534/sin60)
d = 80°
