Let the square side, x be 1 unit.
sin67.5 = a/1
a = 0.92387953251 units.
cos67.5 = b/1
b = 0.38268343237 units.
c = 2b
c = 0.76536686473 units.
d² = 1²+1²
d = √(2) units.
sin67.5...
Let the radius of the semi circle be 1 unit.
cos20 = a/2
a = 1.87938524157 units.
cos20 = 1/b
b = 1.06417777248 units.
c = a-b
c = 0.81520746909 unit.
Where c is AB, the side of the square.
Ar...
Let the square side be 2 units.
Notice;
a+b = c --- (1).
2√(2) = c+a
2√(2)-a = c --- (2).
a² = 2d²
d = (a/√(2)) units.
e = 2-d
e = (2-(a/√(2))) units.
b² = (2-(a/√(2)))²+(a/√(2))²
b² = 4-(4a/√(...
Let the side of the regular pentagon be 1 unit.
Calculating Area Red.
a² = 1²+1²-2*1*1cos108
a = 1.61803398875 units.
b = 108-36-60
b = 12°
(c/sin12) = (1.61803398875/sin96)
c = 0.33826121272 un...
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a² = 15²+12²-2*12*15cos120
a = 23.43074902772 cm.
Where a is the side length of the equilateral triangle ABC.
(23.43074902772/sin120) = (12/sinb)
b = 26.32950349168°
c = 60-b
c = 33.67049650832°...
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...
