Mathematics Question and Solution
Let the side length of the inscribed regular pentagon be 1 unit.
a = ½(120)
a = 60°
b = 180-108
b = 72°
c = 180-60-72
c = 48°
It implies;
(1/sin60) = (d/sin48)
d = 0.8581097301 units.
e = 1+d
e = 1.8581097301 units.
e is the side length of the ascribed regular hexagon.
f² = 0.8581097301²+1.8581097301²-2*0.8581097301*1.8581097301cos120
f = 2.4048671724 units.
Calculating the required angle, Beta. Let it be h.
(2.4048671724/sin120) = (1.8581097301/sinh)
h = 42°
Again, h is the required angle Beta.
