Let b = 1 unit.
(1/sin72) = (a/sin48)
a = 0.78138871113 units.
BD = 1-0.78138871113
BD = 0.21861128887 units.
(AD)² = 1+0.21861128887²-2*0.21861128887cos60
AD = 0.91059299731 units.
Calculating...
a = atan(3/2)°
b = atan(2/3)°
b = Angle BEG.
tan(atan(2/3)) = c/2
⅔ = c/2
c = (4/3) cm.
c = BG.
OG = 2-(4/3)
OG = ⅔ cm.
Notice;
Radius of the circle is 2 cm.
Angle OGH = 180-atan(3/2) = 123.69...
Let DE be 1 unit.
AC = 4 units.
Area ABC is;
8sin60
= 4√(3) square units.
a² = 1+2²-4cos45
a = 1.47362575821 units.
(1.47362575821/sin45) = (1/sinb)
b = 28.6750500631°
c = 60-b
c = 31.32494993...
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a² = √(8)
a = 2√(2) units.
a is the diameter of the orange half circle.
b = ½(a)
b = √(2) units.
b is the radius of the orange half circle.
Calculating c, radius of the inscribed purple circle.
2...
Let the equal lengths be 1 unit.
(1/sin54) = (a/sin84)
a = 1.22929666779 units.
b² = 1.22929666779+1-2*1.22929666779cos126
b = 1.98904379074 units.
Calculating the required angle x.
(1.989043790...
Let the biggest regular pentagon side length be 2 units.
sin72 = a/2
a = 1.90211303259 units.
tan72 = (1.90211303259/b)
b = 0.61803398875 unit.
c = 2b
c = 1.2360679775 units.
Where c is the side...
Angle ABC is;
atan(3/4)°
Therefore;
sin(atan(3/4)) = 3/(BC)
BC = 5 units.
Angle ACB is;
atan(4/3)°
Angle EAC is;
(180-2atan(4/3))°
Calculating CE.
(3/sin(atan(4/3))) = (CE/sin(180-2atan(4/3))...
Let the radius of the 3 congruent circles be r.
Therefore, the general formula for the area of green section is;
½(πr²)-3(60πr²)/360+2(½*r²*sin60)
= ½(πr²)-½(πr²)+r²sin60
= r²sin60
= ½(√(3)r²) squ...
Let BD be 1 unit.
Therefore;
(1/sin100) = (d/sin70)
d = 0.95418889414 units.
(1/sin80) = (AB/sin70)
AB = 0.95418889414 units.
AB is c.
It implies;
d = c.
Calculating a.
(a/sin20) = (0.9541888...
