Calculating Alpha, let it be x.
a = 180-24-54
a = 180-78
a = 102°
Let the side length opposite/facing angle 24° (the shortest length) of the inscribed triangle with angles 24°, 54° and 102°...
Calculating Shaded Area Blue.
Notice.
8 cm is the side length of the ascribed square.
Therefore;
½(8) = 4 cm is the radius of the both inscribed half circles.
tana = 4/8
a = atan(½)...
Calculating Area Red Circle.
Let a be the radius of the inscribed red circle.
b = (4+a) m.
c = (21+a) m.
Therefore;
Calculating a.
a(4+a)+a(21+a)+a(4+21) = (4+a)(21+a)
4a+a²+21a+a²+25a = 84+2...
Calculating Area Ascribed Rectangle.
Let x be the width of the ascribed rectangle.
Let y be the length of the ascribed rectangle.
a = 1+2+1
a = 4 units.
b = (x-2) units.
c = (y-2) u...
Calculating The Required Angle.
Let it be x.
a = ½(12)+b
a = (6+b) cm.
b is the radius of the inscribed sector.
Calculating b.
c² = 6²+12²
c² = 36+144
c = √(180)
c = 6√(5) cm.
I...
Calculating Shaded Fraction.
Let the radius of the inscribed circle be 1 unit.
Therefore, the radius of the inscribed half circle is 2 units.
a² = 2²+(2+2)²
a² = 20
a = 2√(5) units.
a i...
Calculating Inscribed Blue Rectangle Area.
a = 15+5
a = 20 units.
Let b be the length of the blue inscribed rectangle.
b² = 2(20)²-2(20)²cos(90-x)
b² = 800-800(cos90cosx+sin90sinx)
b² =...
Calculating x.
Let a be the side length of the square.
b² = 2a²
b = √(2)a units.
c = ½(b)
c = ½√(2)a units.
a ~ 1
0.5 ~ d
Cross Multiply.
d = 1/(2a) units.
Calculating a.
c+d...
Calculating x.
10² = 18²+x²-2*18xcosy
36xcosy = 224+x²
cosy = (224+x²)/(36x) --- (1).
10² = 6²+x²-2*6xcosy
12xcosy = x²-64
cosy = (x²-64)/(12x) --- (2).
Equating (1) and (2).
(224+x...
Calculating Ratio Purple Area and Orange Area.
Let 2 be the radius of the inscribed orange area.
It implies;
Area orange inscribed circle is;
π(2)²
= 4π square units.
tan30 = 2/a
a = 2√(3) unit...
