Mathematics Question and Solution
Let AB be 1 unit.
(1/sin40) = (BC/sin70)
BC = 1.46190220008 units.
(1.46190220008/sin120) = (AE/sin40)
AE = 1.08506357513 units.
(1.08506357513/sin40) = (CE/sin20)
CE = 0.57735026919 units.
BE = 1.46190220008-0.57735026919
BE = 0.88455193089 units.
(BD)² = 0.88455193089²+0.57735026919²-2*0.57735026919*0.88455193089cos60
BD = 0.77786191343 units.
Therefore angle alpha (angle BDE) is;
Let it be x.
(0.88455193089/sinx) = (0.77786191343/sin60)
x = 80°
Angle alpha (required angle) = 80°
