Mathematics Question and Solution
Calculating L, length of the ascribed regular pentagon.
a = (x+8) units.
b = ⅕(180(5-2))
b = ⅕*180*3
b = 108°
b is the single interior angle of the regular pentagon.
c = 180-b
c = 180-108
c = 72°
Calculating x.
cos72 = x/(x+8)
x = (cos72)x+8cos72
(1-cos72)x = 8cos72
x = 8cos72/(1-cos72)
x = ⅕(8√(5)) units.
x = 3.577708764 units.
Recall.
a = (x+8)
And x = 3.577708764 units.
a = 3.577708764+8
a = 11.577708764 units.
It implies, length L is;
L²+3.577708764² = 11.577708764²
L² = 11.577708764²-3.577708764²
L = √(121.243340224)
L = 11.0110553638 units.
L = 8√(⅕(2√(5))+1) units.
