Mathematics Question and Solution
Let the side length of the inscribed regular hexagon which is equal the side length of the ascribed regular nonagon be 1 unit.
a = ⅙*180(6-2)
a = 120°
a is the single interior angle of the inscribed regular hexagon.
b = ⅑*180(9-2)
b = 140°
b is the single interior angle of the ascribed regular nonagon.
c = 140-120
c = 20°
d = 180-20-60
d = 100°
(1/sin100) = (e/sin20)
e = 0.3472963553 units.
(1/sin100) = (f/sin60)
f = 0.8793852416 units.
g = 1-f
g = 0.1206147584 units.
cos80 = h/0.1206147584
h = 0.020944533 units.
j = 2h
j = 0.041889066 units.
sin50 = k/1
k = sin50 units.
l = 1+2k
l = 2.5320888862 units.
m = l+j
m = 2.5739779522 units.
n = m-1-0.3472963553
n = 1.2266815969 units.
o² = 1.2266815969²+1²-2*1.2266815969*1cos60
o = 1.1305158748 units.
Therefore, the required angle is;
Let it be p.
(1.1305158748/sin60) = (1/sinp)
p = asin(sin60/1.1305158748)
p = 50°
Again, p is the required angle.
