Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the two equal lengths be 1 unit.
(a) Calculating Theta exactly.
Let theta be x.
Calculating x.
x = ½(90-54)
x = ½(36)
x = 18°
sin18 = a/1
a = 0.30901699437 unit.
b = 90-18
b = 72°
sin72 = c/1
c = 0.9510565163 unit.
tan36 = 0.9510565163/d
d = 1.30901699437 units.
Area Blue is;
0.5(1.30901699437*0.9510565163)
= 0.62247457122 square units.
e = 270-54-96
e = 120°
f = 360-120-72
f = 168°
g² = 2-2cos168
g = 1.98904379074 units.
h = ½(180-168)
h = 6°
(1.98904379074/sin54) = (i/sin24)
i = 1 units.
Area ABCDE is;
0.5(1*1.98904379074)sin102 - 0.5sin168
= 0.97278920583 - 0.10395584541
= 0.86883336042 square units.
(b) Area Blue ÷ Area ABCDE to 2 decimal places is;
0.62247457122 ÷ 0.86883336042
= 0.71644874561
≈ 0.72
