Mathematics Question and Solution
Let the side length of the regular pentagon be 1 unit.
x² = 2-2cos30
x = 0.5176380902 units.
y = 108-90
108° is the single interior angle of the regular pentagon.
y = 18°
c = y+½(180-30)
c = 18+75
c = 93°
d² = 1²+0.5176380902²-2*0.5176380902*1cos93
d = 1.1498397111 units.
d is a plus b (a+b).
(1.1498397111/sin93) = (1/sine)
e = 60.2841662413°
f = 180-75-e
f = 44.7158337587°
Calculating a.
(a/sin75) = (0.5176380902/sin44.7158337587)
a = 0.7106400231 units.
Notice!
a+b = d
a+b = 1.1498397111
And a is 0.7106400231 units.
It implies;
0.7106400231+b = 1.1498397111
b = 1.1498397111-0.7106400231
b = 0.439199688 units.
Therefore;
a/b is;
0.7106400231÷0.439199688
= 1.6180339889
= ½(1+√(5))
