Mathematics Question and Solution
Let 1 unit be the side length of the regular hexagon.
a = ⅙*180(6-2)
a = 120°
a is the single interior angle of the regular hexagon.
cos75 = 0.5/b
b = 1.93185165258 units.
c² = 1²+0.5²-2*1*0.5cos120
c = 1.32287565553 units.
d = 120-75
d = 45°
(0.5/sine) = (1.32287565553/sin120)
e = 19.1066053506°
f = 120-e
f = 100.893394649°
g = 360-120-100.893394649-75
g = 64.106605351°
h = 90-g
h = 25.893394649°
j² = 1.32287565553²+1.93185165258²-2*1.32287565553*1.93185165258cos25.893394649°
j = 0.94019923219 units.
k² = 1.32287565553²+(1.93185165258*0.5)²-2*1.32287565553*0.5*1.93185165258cos25.893394649°
k = 0.61965683746 units.
(0.61965683746/sin25.893394649) = (1.32287565553/sinl)
l = 111.206023113°
m = 180-l
m = 68.793976887°
Therefore, the required angle theta is;
Let it be n.
n = 180-45-m
n = 135-68.793976887
n = 66.206023113°
