Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the single side length of triangle ABC be 2 units.
Calculating Area ABC.
½(4sin60)
= √(3) square units.
Calculating Area Yellow.
It is;
Area equilateral triangle with side 2 units - Area triangle with two lengths 2 units and (√(2)/sin75) units, and angle 60°, the angle they form - Area triangle with two lengths 1 units and (1/sin105) units, and angle 15°, the angle they form.
= √(3) - (√(6)/2sin75) - (sin15/(2sin105)
= (√(3) - (√(6)/(2sin75)) - (sin15/(2sin105))) square units.
= 0.33012701892 square units.
Therefore;
Area yellow ÷ Area ABC is;
= 0.33012701892/√(3)
= 0.19059892324
