Let the side length of triangle ABC be 1 unit.
a = 120-78
a = 42°
b = 60-42
b = 18°
(1/sin42) = (c/sin18)
c = 0.4618186516 unit.
tan60 = d/0.5
d = 0.86602540378 unit.
Area Green is;
0.5*0.4618...
Let the inscribed square side be a.
Radius of the half circle is 5 units.
Considering Similar Triangle Ratios.
5 = a
a = (5-a)
Cross Multiply.
25-5a = a²
a²+5a-25 = 0
(a+(5/2))² = 25+(5/2)²
a+(5/2...
Notice;
The figure is not drawn to scale.
Let BC be 1 unit.
(1/sin135) = (a/sin30)
a = 0.70710678119 units.
(1/sin135) = (b/sin15)
b = 0.36602540378 units.
Notice;
MB = NC, let it...
Let AB be 1 unit.
(1/sin100) = (b/sin30)
b = 0.50771330594 units.
(1/sin110) = (d/sin30)
d = 0.53208888624 units.
d is CB.
(0.50771330594/sin30) = (c/sin50)
c = 0.77786191343 units.
a² = 0.7778...
Notice;
The inscribed star is formed from a pentagram (a regular pentagon is ascribing the star).
Let the side of the pentagram be 1 unit.
tan54 = a/0.5
a = 0.68819096024 unit.
cos54 = 0.5/b
b =...
Let the inscribed purple regular heptagon side be 1 unit.
a = ⅐(180*5)
a = ⅐(900)°
b = 180-⅐(900))
b = ⅐(360)°
c = 180-2(⅐(360))
c = ⅐(540)°
(1/sin⅐(540)) = (d/sin⅐(360))
d = 0.8019377358 unit....
Let the congruent lengths be 1 unit.
(1/sin50) = (a/sin80)
a = 1.28557521937 units.
sin(60) = b/2
b = √(3) units.
b = 1.73205080757 units.
c = 20°
d² = 1.73205080757²+1.28557521937²-2*1.73205080...
Let the square side length be 1 unit.
Therefore, the regular hexagon side length is 1 unit as well.
sin30 = a/1
a = 0.5 units.
b = 1+a
b = 1+0.5
b = 1.5 units.
cos30 = c/1
c = ½√(3) units.
d =...
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Let the height and base of area triangle C be 2 units and 3 units respectively.
Therefore;
Area Triangle C is;
½*2*3
= 3 square units.
tana = (2/3)
a = atan(2/3)°
b = 189-a
b = 180-atan(2/3)
b...
