Mathematics Question and Solution
Let 1 be the side length of the ascribed regular hexagon.
a = ⅙*180(6-2)
a = 120°
a is the single interior angle of the ascribed regular hexagon.
b² = 1²+1²-2*1*1cos120
b = 1.7320508076 units.
b = √(3) units.
c = ½(180-120)
c = 30°
d = 75-30
d = 45°
sin75 = √(3)/e
e = 1.7931509443 units.
f = ½(e)
f = 0.8965754722 units.
g² = 1.7931509443²+1.73205080762-2*1.7931509443*1.7320508076cos45
g = 1.350216821 units.
h = 120-75
h = 45°
(1.350216821/sin45) = (1.7931509443/sinj)
j = 69.8960906364°
k = 180-j
k = 110.1039093636°
l = 180-45-110.1039093636
l = 24.8960906364°
(m/sin24.8960906364) = (1.350216821/sin45)
m = 0.8038475772 units.
n² = 0.8038475772²+0.8965754722²-2*0.8038475772*0.8965754722cos45
n = 0.6563387984 units.
Therefore, the required angle, theta is;
Let it be o.
(0.6563387984/sin45) = (0.8965754722/sino)
o = 75°
Again, o is the required angle theta.
