Mathematics Question and Solution
Let the base of the triangle ascribing the green and yellow area b 1 unit.
tan55 = a/1
a = 1.42814800674 units.
tan55 = b/(1-b)
b = 0.58816349035 unit.
Where b is the side of the white and yellow square.
c = 1-b
c = 0.41183650965 unit.
sin55 = d/0.58816349035
d = 0.4817953255 unit.
tan35 = 0.4817953255/e
Where e is the side of the blue area.
e = 0.68807503377 unit.
Area Blue is;
e² = 0.68807503377²
= 0.47344725209 square units.
sin35 = 1/f
f = 1.74344679562 units.
g = f-0.68807503377
g = 1.05537176185 units.
Let the yellow and green square side be h.
tan55 = i/(h-0.4817953255)
i = (htan55-0.68807503377) unit.
tan35 = j/h
j = 0.70020753821h unit.
It implies;
i + h + j = 1.05537176185
(htan55-0.68807503377)+h+0.70020753821h = 1.05537176185
3.12835554495h = 1.74344679562
h = 0.55730455524 unit.
sin55 = 0.58816349035/k
k = 0.71801504306 unit.
tan55 = 0.55730455524/l
l = 0.39022885066 unit.
m = l+0.55730455524
m = 0.9475334059 unit.
n = m-0.71801504306
n = 0.22951836284 unit.
tan55 = o/0.22951836284
o = 0.3277861924 unit.
Area Green is;
½(n*o)
= 0.5(0.22951836284*0.3277861924)
= 0.03761647512 square units.
Therefore;
Area Blue ÷ Area Green to 1 decimal place is;
0.47344725209 ÷ 0.03761647512
= 12.58616737935
≈ 12.6
