Mathematics Question and Solution
Calculating r, radius of the inscribed circle.
a = ½(108)
a = 54°
a is half the single interior angle of the regular pentagon.
tan54 = r/b
b = r/tan54
b = 0.726542528r units.
r is the radius of the inscribed circle.
c = 6-b
c = (6-0.726542528r) units.
It implies;
tan(0.5*54) = r/c
tan27 = r/(6-0.726542528r)
r = 6tan27-0.726542528tan(27)r
r = 3.057152697-0.3701919082r
r+0.3701919082r = 3.057152697
1.3701919082r = 3.057152697
r = 3.057152697/1.3701919082
r = 2.2311857768 units.
