Let AB be 1 unit.
(1/sin150) = (a/sin20)
a = 0.68404028665 units.
a is AD.
Notice;
AB = AC = 1 unit.
(CD)² = 1+0.68404028665²-2*0.68404028665cos30
CD = 0.53208888624 units.
Therefore, the requi...
Let the radius of the green circle be r.
sina = (3+2√(3))/(6+4√(3))
a = asin(½)
a = 30°
It implies;
cos30 = (3+2√(3))/((3+2√(3))+r)
6+4√(3) = 3√(3)+6+√(3)r
√(3) = √(3)r
r = 1 unit.
(3/sin108) = (EG/sin18)
EG = 0.9747590887 units.
(3/sin108) = (EF/sin54)
EF = 2.55195242506 units.
AF = 4-2.55195242506
AF = 1.44804757494 units.
sin18 = a/1.44804757494
a = 0.44747130932 units....
Let the height and base of the rectangle be x and y respectively.
Let the inscribed circle's radius be r.
Therefore;
0.5xy = 36
xy = 72 square units.
Therefore;
y = 72/x --- (1)....
Let the radius of the large circle be 1 unit.
Diameter of the large circle = 2 units.
sin60 = 2/a
a = ⅓(4√(3)) units.
Where a is the side length of triangle ABC.
b² = 2-2cos
b = √(3) units.
c =...
Let the regular pentagon side be 1 unit.
sin54 = a/1
a = 0.80901699437 unit.
b = 2a
b = 1.61803398875 units.
Let the regular hexagon side be c.
Calculating c.
c+2(csin30) = b
c+2(0.5c) = 1.6180...
Radius of the semi circle is 12 cm.
Angle AED = atan(½)°
sin(atan½) = a/24
a = 10.733126292 cm.
a = AF.
cos(atan½) = b/12
b = 21.466252584 cm.
b = EF.
cos(atan2) = c/10.733126292
c = 4.8 cm.
d...
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a² = 2*12²-2*12²cos120
a = 12√(3) cm.
a = 20.78460969083 cm.
a = AB.
b = 2a
b = 24√(3) cm.
b = 41.56921938165 cm.
b = AC.
c² = 12²+41.56921938165²-24*41.56921938165cos30
c = 31.74901573277 cm.
c =...
Let the regular octagon side be 2 units.
Area Octagon is;
½(8*2)*(2/(2tan(180/8)))
= 8/(tan(180/8))
= 19.31370849898 square units.
Calculating Area Red.
a = ⅛(180*6)
a = 135°
Let the square...
