Mathematics Question and Solution
Let the side length of the regular hexagon be 1 unit.
a = ⅙(180(6-2))
a = ⅙(180*4)
a = 120°
a is the single interior angle of the regular hexagon.
b² = 1+1-2cos120
b = 2-2cos120
b = √(3) units.
b is the height of the regular hexagon.
sin75 = √(3)/c
c = 1.7931509443 units.
c is the green length.
d = ½(1.7931509443)
d = 0.8965754722 units.
d is half c.
e = 90-75
e = 15°
sin15 = f/1.7931509443
f = 0.4641016151 units.
g = 1-f
g = 1-0.4641016151
g = 0.5358983849 units.
h² = 1+0.5358983849²-2*0.5358983849cos120
h = 1.350216821 units.
h is a yellow length.
j = 120-75
j = 45°
(1.350216821/sin45) = (1.7931509443/sink)
k = 69.8960906325°
l = 180-k
l = 180-69.8960906325
l = 110.1039093675°
m = 180-110.1039093675-45
m = 24.8960906325°
(n/sin24.8960906325) = (1.350216821/sin45)
n = 0.8038475771 units.
o² = 0.8038475771²+0.8965754722²-2*0.8038475771*0.8965754722cos45
o = 0.6563387984 units.
It implies;
The required angle is;
Let it be p.
(0.8965754722/sinp) = (0.6563387984/sin45)
Therefore;
p (required angle) = 75.0000000187°
p = 75°
