Let the equal lengths be 1 unit.
(1/sin54) = (a/sin84)
a = 1.22929666779 units.
b² = 1.22929666779+1-2*1.22929666779cos126
b = 1.98904379074 units.
Calculating the required angle x.
(1.989043790...
Let the biggest regular pentagon side length be 2 units.
sin72 = a/2
a = 1.90211303259 units.
tan72 = (1.90211303259/b)
b = 0.61803398875 unit.
c = 2b
c = 1.2360679775 units.
Where c is the side...
Angle ABC is;
atan(3/4)°
Therefore;
sin(atan(3/4)) = 3/(BC)
BC = 5 units.
Angle ACB is;
atan(4/3)°
Angle EAC is;
(180-2atan(4/3))°
Calculating CE.
(3/sin(atan(4/3))) = (CE/sin(180-2atan(4/3))...
Let the radius of the 3 congruent circles be r.
Therefore, the general formula for the area of green section is;
½(πr²)-3(60πr²)/360+2(½*r²*sin60)
= ½(πr²)-½(πr²)+r²sin60
= r²sin60
= ½(√(3)r²) squ...
Let BD be 1 unit.
Therefore;
(1/sin100) = (d/sin70)
d = 0.95418889414 units.
(1/sin80) = (AB/sin70)
AB = 0.95418889414 units.
AB is c.
It implies;
d = c.
Calculating a.
(a/sin20) = (0.9541888...
Let r be 1 unit.
Calculating R.
(R+1)² = x²+(R-1)²
Calculating x.
x² = R²+2R+1-R²+2R-1
x = √(4R)
x = 2√(R) units.
It implies;
(2R)² = (2√(R))²+2²
4R² = 4R+4
R²-R-1= 0
Solving the quadratic equ...
Let the two congruent lengths be 1 unit.
(1/sin50) = (a/sin80)
a = 1.28557521937 units.
(1.28557521937/sin110) = (b/sin60)
b = 0.46791111376 units.
(1/sin70) = (c/sin80)
c = 1.04801052092 units....
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The side length of the congruent Hexagons is 2 unit.
Area hexagon is;
(6*2²)/(4tan30)
= 6√(3)) square units.
a² = 8-8cos30
a = √(8-4√(3)) unit.
Area ABC is;
½(√(8-4√(3)))²sin60
= (2√(3)-3) squa...
25 = 49+64-14*8cosa
112cosa = 113-25
a = acos(88/112)
a = 38.21321070174°
a = Angle ACB.
5b+7b+8b = 56sin38.21321070174
b = (56sin38.21321070174)/20
b = √(3) cm
b = 1.73205080757 cm.
b = radius o...
