Let AB be 1 unit.
a = 180-12-36-18
a = 180-66
a = 114°
a is angle AEB.
(1/sin114) = (b/sin(18+36))
b = 0.885579352 units.
b is AE.
c = 180-6-36-42
c = 96°
(1/sin96) = (d/sin(42+36...
a = ½(90)
a = 45°
tanb = 2/1
b = atan(2)°
c = 90-b
c = atan(½)°
d = a-c
d = (45-atan(½))°
e = 180-2d
e = 180-2(45-atan(½))
e = (90+2atan(½))°
Therefore, length EF, let it be f,...
a = 7-2.5
a = 4.5 units.
b = 7+1
b = 8 units.
tanc = 4.5/8
c = atan(4.5/8)°
tand = 4.5/3
d = atan(4.5/3)°
e = 180-c-d
e = (180-atan(4.5/8)-atan(4.5/3))°
(4/sin(180-atan(4.5/8)-a...
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Calculating the red angle (angle DAM).
Notice!
ABCD is a regular quadrilateral (square).
Let AB be 1 unit.
tan60 = AB/BK
BK = 1/√(3)
BK = ⅓√(3) units.
CK = 1-BK
CK = ⅓(3-√(3)) uni...
Calculating angle x.
tana = ⅗
a = atan(⅗)°
tan = ⅘
b = atan(⅘)°
c = atan(5/4)°
Therefore, the required angle x is;
x = a+c
x = atan(⅗)+atan(5/4)
x = (atan(⅗)+atan(5/4))°
x = 82....
Calculating the radius of the small inscribed pink circle. Let it be r.
b = ⅕*180(5-2)
b = 108°
b is the single interior angle of the ascribed regular pentagon.
c² = 10²+10²-2*10*10cos108...
Notice!
The ascribed polygon is a regular dodecagon (12 sides and 12 interior angles equal).
It's since interior angle is;
a = 180(12-2)/12
a = 1800/12
a = 150°
The middle inscribed polyg...
Calculating x.
Notice!
Diameter of the ascribed circle is 10 cm.
It's radius, a is;
a = ½(10)
a = 5 cm.
Let b be the radius of the inscribed circle.
c = b-4
c = 1 cm.
d = (5-b) c...
a = 2*135
a = 270°
a is reflex angle BOE.
b = 360-a
b = 90°
b is angle BOE.
c² = 6²+2-2*6√(2)cos135
c = 7.0710678119 units.
c = 5√(2) units.
c is BE.
Notice!
Since angle BOE is 9...
