Let the two congruent lengths be 1 unit.
tan40 = a/1
a = 0.83909963118 unit.
cos40 = 1/b
b = 1.30540728933 units.
Calculating r, radius of the red inscribed circle.
(r/tan(20)) + (r/t...
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...
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 = 0.33...
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 = 33.67...
Sir Mike Ambrose is the author of the question.
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.
tan6...
a² = 12²+6²
a = 6√(5) cm.
a = AE.
b = atan(1/2)°
b = angle DAE.
c = 180-atan(2)
c = 116.56505117708°
c = angle AFC.
d = 180-116.56505117708-atan(1/2)
d = 36.86989764584°
(6/sin36....
Le the side of the pentagram be 1 unit.
tan54 = a/0.5
a = 0.68819096024 unit.
cos54 = 0.5/b
b = 0.85065080835 unit.
c = b+a
c = 1.53884176859 units.
Let the side length of the ascrib...
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 = 0.8019...
Let the side of the regular pentagon be 1 unit.
a² = 2-2cos108
a = 1.61803398875 units.
sin30 = b/0.5
b = 0.25 unit.
c = 2b
c = 0.5 unit.
Where c is the inscribed square side.
Are...
a = asin(1/3)°
a = 19.47122063449°
a = angle ABF.
Let the centre of the diameter of the half circle be O.
Angle AOF = 90-19.47122063449 = 70.52877936551°
(OC)² = 12²+18²
OC = 6√(13) c...
