Mathematics Question and Solution
Notice;
AB = AC
(6.84/sin40) = (a/sin70)
a = 9.99941104856
a = 10 cm.
a is AB = AC.
(9.99941104856/sin155) = (b/sin15)
b = 6.12381965823 cm.
(9.99941104856/sin155) = (c/sin10)
c = 4.10862393682 cm.
d = 70-15
d = 55°
Area Green is;
0.5*6.84*4.10862393682sin55
= 11.51030992395 cm²
e = 9.99941104856-6.84
e = 3.15941104856 cm.
Area Orange is;
0.5*3.15941104856*6.12381965823sin30
= 4.8369158719 cm²
It implies;
Area Orange ÷ Area Green to 2 decimal places is;
4.8369158719÷11.51030992395
= 0.42022464242
≈ 0.42
Calculating Angle Alpha to 1 decimal place.
Let it be x.
x = f+g
Calculating f.
f² = 3.15941104856²+6.12381965823²-2*3.15941104856*6.12381965823cos30
f = 3.73790171246 cm.
(3.73790171246/sin30) = (3.15941104856/sinf)
f = 25°
Calculating g.
h² = 6.84²+3.73790171246²-2*6.84*3.73790171246cos55
h = 5.60606524674 cm.
(5.60606524674/sin55) = (6.84/sinj)
j = 88.10520480362°
j is the supplementary angle of g.
g+j = 180
g = 180-j
g = 180-88.10520480362
g = 91.89479519638°
Therefore;
x = 25+91.89479519638
x = 116.89479519638°
x ≈ 116.9°
