Mathematics Question and Solution
Let the side length of the regular octagon be 1 unit.
a = ⅛(180(8-2))
a= ⅛(180*6)
a = 135°
a is the single interior angle of the regular octagon.
2b² = 1²
b = √(1/2)
b = ½√(2) units.
c = 2b+1
c = 2(½√(2))+1
c = (√(2)+1) units.
c is the side length of the regular triangle (equilateral triangle).
d² = 2-2cos135
d = Let the side length of the regular octagon be 1 unit.
a = ⅛(180(8-2))
a= ⅛(180*6)
a = 135°
a is the single interior angle of the regular octagon.
2b² = 1²
b = √(1/2)
b = ½√(2) units.
c = 2b+1
c = 2(½√(2))+1
c = (√(2)+1) units.
c is the side length of the regular triangle (equilateral triangle).
d² = 2-2cos135
d = 1.847759065 units.
e = 60+90-22.5
e = 127.5°
Therefore;
f² = 2.4142135624²+1.847759065²-2*1.847759065*2.4142135624cos127.5
f = 3.8306487878 units.
(3.8306487878/sin127.5) = (1.847759065/sing)
g = 22.5°
Therefore, the required angle, let it be h is;
h = 60-2g
h = 60-2(22.5)
h = 60-45
h = 15°
