Mathematics Question and Solution
sin30 = 1/a
½ = 1/a
a = 2 units.
cos30 = ½(a)/b
½√(3) = 1/b
√(3)b = 2
b = ⅓(2√(3))
b = ⅓(2√(3)) units.
b = 1.1547005384 units.
b is the radius of the ascribed semi circle.
Calculating c, radius of the inscribed green semi circle.
d = 2b-c
d = (⅓(4√(3))-c) units.
sin30 = c/d
½ = c/(⅓(4√(3))-c)
2c = ⅓(4√(3))-c
9c = 4√(3)
c = ⅑(4√(3)) units.
Again, c is the radius of the inscribed green semi circle.
Area inscribed green semi circle is;
½(c)²
= ½*⅑(4√(3))*⅑(4√(3))π
= 8π/27 square units.
Area yellow is;
(½*⅓(2√(3))*⅓(2√(3))π)-Area Green.
= ⅓(2π)-(8π/27)
= (18π-8π)/27
= (10π/27 square units.
Therefore;
Area Green/Area Yellow in percentage is;
((8π/27)/(10π/27))*100
= (4/5)*100
= 80%
