a² = 5-4cos120
a = √(7) units.
(√(7)/sin120) = (2/sinb)
b = 40.89339464913°
c = 180-2*40.89339464913
c = 98.21321070174°
Calculating r.
0.5*r(r-1)sin98.21321070174 +(3/2) = (98.21321070174π*r²)...
Let the side length of the regular pentagon be 1 unit.
c² = 2-2cos108
c = 1.61803398875 units.
(d/sin36) = (1/sin108)
d = 0.61803398875 units.
e = c-d
e = 1 unit.
Calculating a.
sin72 = a/1
a =...
Sir Mike Ambrose is the author of the question.
Let the two equal length be 2 units each.
2 = 2/a
a = 1 unit.
sin(atan(½)) = b/3
b = ⅕(3√(5)) units.
c = 2b
c = ⅕(6√(5)) units.
Where c is the squa...
Calculating equation of the curve.
2a² = 4²
a = 2√(2)
b = (4+2√(2))
b is the maximum turning point.
Therefore considering points;
(0, 0) and ((4+2√(2)), (4+2√(2)))
y-(4+2√(2)) = c(x-(4+2√(2)))²...
Sir Mike Ambrose is the author of the question.
Aqua total in cm² is;
tan30 = a/10
a = ⅓(10√(3)) cm.
sin60 = 2/b
b = ⅓(4√(3)) cm.
c = a+b
c = ⅓(14√(3)) cm.
tan30 = d/2
d = ⅓(2√(3)) cm.
e = c-d...
Sir Mike Ambrose is the author of the question.
Let r be the radius of the circle.
Calculating r.
5.5²+(√(r²-2.5²)-4)² = r²
r = ½(5√(5)) units.
a = √((5√(5)/2)²-(5/2)²)-4)²
a = 1 unit.
b = 180-...
Let AC be 2 units.
It implies;
OA = AB = BC = DE = EF = 1 unit.
Blue length = 1 unit.
Calculating red length.
a² = 5-4cos72
a = 1.94008557092 units.
a is OD.
(1.94008557092/sin72) = (1/sinb)
b...
Let the blue diagonal be 1 unit.
(1/sin110) = (a/sin30)
a = 0.53208888624 units.
(1/sin70) = (b/sin40)
b = 0.68404028665 units.
c² = 0.68404028665²+0.53208888624²-2*0.68404028665*0.532088...
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Calculating r.
a = √(2)r units.
b = 2√(2)r units.
c = 3r units.
d = √(2) units.
It implies;
a+b+c = d
√(2)r+2√(2)r+3r = √(2)
r(3+3√(3)) = √(2)
r = √(2)/(3+3√(2))
r = (3√(2)-6)/(9-18)
r = (3√(2)-6...
