Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
a = 4/2tan(180/9)
a = 2/tan20 units.
b = 4/2tan(180/6)
b = 2/tan30 units.
Therefore;
Red Length is;
a+b
= (2/tan20)+(2/tan30)
= 2(tan20+tan30)/(tan20tan30) units.
c = 2+b
c = 2+2/tan30
c = (2tan30+2)/tan30
(a) Length Red ÷ Length Blue exactly is;
(2(tan20+tan30)/(tan20tan30)) ÷ ((2tan30+2)/tan30)
= 2(tan20+tan30)/2(tan20tan30+tan20)
= (tan20+tan30)/tan20(tan30+1)
(b) Calculating Orange Area.
d = 360-140-120
d = 100°
e² = 32-32cos100
e = √(32-32cos100) units.
e = 6.12835554495 units.
(6.12835554495/sin100) = (4/sinf)
f = 40°
g = 360-120-90-40
g = 110°
Therefore;
Area Orange exactly is;
½(4²)sin100+½*4√(32-32cos100)sin110
= 8sin100+2√(32-32cos100)sin110
= 2(4sin100+√(32-32cos100)sin110) square units.
= 19.39600299038 square units exactly in decimal.
