Mathematics Question and Solution
a = 360-140-80
a = 140°
cos20 = 1/b
b = 1.06417777248 units.
(1.06417777248/sin30) = (c/sin70)
c = 2 units.
d² = 4+1.064177772482²-4*1.06417777248cos140
d = 2.89711998506 units.
(2.89711998506/sin140) = (2/sine)
e = 26.34291130662°
f = 40-e
f = 13.65708869338°
g = 20+26.34291130662
g = 46.34291130662°
tan46.34291130662 = h/2
h = 2.09602104183 units.
Area ABC is;
0.5*2*2.09602104183
= 2.09602104183 square units.
Calculating Area Blue.
i = 60-26.34291130662
i = 33.65708869338=
(1.06417777248/sin120) = (j/sin33.65708869338)
j = 0.68103067617 unit.
tan20 = k/2
k = 0.72794046853 unit.
Area Blue is;
0.5*0.72794046853*1.06417777248sin70+0.5*1.06417777248*0.68103067617sin26.34291130662
= 0.52476868975 square units.
Area Blue ÷ Area ABC is;
0.52476868975÷2.09602104183
= 0.25036422788
≈ 0.25
