Mathematics Question and Solution
Let the side of the three inscribed congruent regular hexagon be 1 unit.
It implies, the side length of the square is;
a = 6 units.
b² = 2-2cos120
b = √(3) units.
c = 1+(½)
c = ½(3) units.
c = 1.5 units.
d = ½+2
d = ½(5) units.
d = 2.5 units.
e = a-b
e = (6-√(3)) units.
f = 6-c
f = 6-½(3)
f = ½(12-3)
f = ½(9) units.
f = 4.5 units.
It implies, the required angle x, is;
atan((2.5)/(6-√(3)))+x+atan((6-√(3))/4.5) = 90
x = 90-atan((2.5)/(6-√(3)))-atan((6-√(3))/4.5)
x = 16.1558984641°
