Mathematics Question and Solution
Let the red square side be 1 unit.
Area Red is;
1² = 1 square units.
Calculating Area Blue.
(1/sin30) = (a/sin126)
a = 1.6180339887 units.
a = 2sin126 units.
It implies;
Area Blue is;
0.5*2sin126sin24
= sin24sin126 square units.
Therefore;
Area Blue ÷ Area Red exactly is;
sin24sin126÷1
= sin24sin126
= 0.3290568565 exactly in decimal.
Calculate Alpha to 1 decimal place.
b = 180-100
b = 80°
c = 126-80
c = 46°
(1/sin30) = (d/sin24)
d = 0.8134732862 units.
(0.8134732862/sin30) = (e/sin70)
e = 1.5288296884 units.
f² = 1+1.5288296884²-2*1.5288296884cos46
f = 1.1014951366 units.
(1.1014951366/sin46) = (1/sing)
g = 40.7725325353°
h = 180-46-40.7725325353
h = 93.2274674647°
It implies;
Angle Alpha to 1 decimal place is;
h-24
= 93.2274674647-24
= 69.2274674647°
≈ 69.2°
It implies;
Alpha ≈ 69.2°
Area Blue/Area Red exactly is;
= sin24sin126
= 0.3290568565 exactly in decimal.
