Mathematics Question and Solution
a = ⅛*180(8-2)
a = 135°
a is the single interior angle of the regular octagon.
b² = 2²+2²-2*2*2cos135
b = 3.69551813 units.
c = 135-2*½(180-135)
c = 135-45
c = 90°
d = 90-½(45)
d = 90-22.5
d = 67.5°
(e/tan45)+(e/tan33.75) = 3.69551813
2.4966057627e = 3.69551813
e = 1.480216935 units.
e is the radius of the inscribed circle.
f² = 2*1.480216935²
f = 2.0933428647 units.
g = 67.5-½(360-2*135)
g = 67.5-45
g = 22.5°
2h² = 2²
h = √(2) units.
j = ½(2h+2)
j = (√(2)+1) units.
j = 2.4142135624 units.
k² = 2.0933428647²+2.4142135624²-2*2.0933428647*2.4142135624cos22.5
k = 0.9339966274 units.
It implies, the required length, x is;
x = e+k
x = 1.480216935+0.9339966274
x = 2.4142135624 units.
x = (√(2)+1) units.
