Mathematics Question and Solution
Please, move a step right to view the analyzed figure.
Notice;
ABC triangle is Isosceles.
a² = 3²-2²
a = √(5) units.
Where a is AD.
tanb = ½(√(5))°
b = atan(½(√(5)))°
b = 48.18968510422°
Where b is angle ACB.
c = 0.5(180-48.18968510422)
c = 65.90515744789°
Where c is angle ABC.
d = 90-65.90515744789
d = 24.09484255211°
Where d is angle BAD
cos65.90515744789 = e/3
e = 1.22474487139 units.
Where e = x = BF.
tan24.09484255211 = f/1.22474487139
f = 0.54772255751 units.
Where f is FG.
It implies;
Area yellow Inscribed triangle is;
0.5*0.54772255751*1.22474487139
= 0.33541019663 square units.
Area blue is;
Area triangle ABC - Area yellow Inscribed triangle.
= (0.5*3*3sin48.18968510422) - (0.33541019663)
= 3.01869176962 square units.
Therefore;
Area Blue ÷ Area Yellow is;
3.01869176962÷0.33541019663
= 8.99999999985
= 9
