Mathematics Question and Solution
Let a side length of the three congruent regular pentagon be 1 unit.
Single interior angle of the three congruent regular pentagon is;
⅕(180*3)
= 108°
a² = 1²+0.5²-2*1*0.5cos108
a = 1.24860602048 units.
(1.24860602048/sin108) = (1/sinb)
b = 49.6138224408°
c² = 2-2cos108
c = 1.61803398875 units.
d = c+1+1
d = 3.61803398875 units.
e² = 1+3.61803398875²-2*3.61803398875cos108
e = 4.04057395938 units.
(4.04057395938/sin108) = (1/sinf)
f = 13.6138224408°
g = 180-108-13.6138224408
g = 58.3861775592°
Therefore, the proof.
(180-b-g) must equal w.
Where w is 72°
It implies;
180-49.6138224408-58.3861775592
= 180-108
= 72° which is w.
Proved!
