Mathematics Question and Solution
cos30 = a/16
a = 8√(3) cm.
cos30 = 10/b
b = ⅓(20√(3)) cm.
c = a-b
c = 8√(3)-⅓(20√(3))
c = ⅓(4√(3)) units.
d = 2c
d = ⅓(2√(3)) cm.
e = b+d
e = ⅓(20√(3))+⅓(2√(3))
e = ⅓(22√(3)) cm
e = 12.7017059222 cm.
f² = 12.7017059222²+8²-16*12.7017059222cos30
f = 7.0237691686 cm.
(7.0237691686/sin30) = (8/sing)
g = 34.7150039538°
h = 180-120-g
h = 25.2849960462°
tan25.2849960462 = 2/j
j = 4.233901974 units.
tan30 = k/10
k = ⅓(10√(3)) cm.
l = k-j
l = 1.5396007179 cm.
Area red is;
0.5*1.5396007179*⅓(2√(3))sin120
= 0.769800359 cm²
Area yellow is;
(0.5*12.7017059222*8sin30) - Area Red
= (0.5*12.7017059222*8sin30)-0.769800359
= 24.6336114854 cm²
It implies;
Area yellow ÷ Area red is;
24.6336114854÷0.769800359
= 31.9999999966
= 32
