Mathematics Question and Solution
Let AB be 2 units.
Therefore;
BC = 1 unit.
tan30 = a/3
a = √(3) units.
tan30 = b/1
b = ⅓(√(3)) units.
c = a-b
c = ⅔(√(3)) units.
d² = (⅓√(3))²+1²
d = ⅔(√(3)) units.
sin60 = ⅔*√(3)/e
e = ⅓(4) units.
sin30 = f/⅔(√(3))
f = ⅓(√(3)) units.
sin60 = g/⅔(√(3))
g = 1 unit.
h = e-g
h = ⅓ unit.
tani = (⅔*√(3))/(⅓(4))
i = atan(√(3)/2)°
tan(atan(√(3)/2)) = j/(⅓)
j = ⅙(√(3)) unit.
l = j+b
= ½(√(3)) unit.
Therefore;
Area Yellow is;
½*1(⅙(√(3))+⅔(√(3)))
= ½*⅙(5√(3))
= 5√(3)/12 square units.
Area Green is;
½(½(√(3))*⅓)
= √(3)/12 square units.
It implies;
Area Yellow ÷ Area Green exactly is;
(5√(3)/12) ÷ (√(3)/12)
= 5
