Let a be the side of the inscribed square.
24² = a²+(2a)²
576 = a²+4a²
576 = 5a²
a = √(576/5)
a = 10.733126292 cm.
b = ½(24-10.733126292)
b = 6.633436854 cm.
b = AM = DR.
c = atan(6.633436854/(...
AB = BC = AC = 6 cm.
cos60 = 2/BE
BE = 4 cm.
(DE)² = 4²-2²
DE = 2√(3) cm.
(CE)² = (2√(3))²+4²
CE = 12+16
CE = 2√(7) cm
EF = (2√(7)-4) cm.
EF = 1.29150262213 cm.
AE = 6-4
AE = 2 cm.
Angle AEF =...
Let CE be 2 units.
Let the square side be a.
b =√(2)a unit.
c = (√(2)a-2) units.
Calculating a
2²+2² = (√(2)a-2)²
8 = 2a²-4√(2)a+4
2a²-4√(2)a-4 = 0
a²-2√(2)a-2 = 0
(a-√(2))² = 2+2
a = √(2)±2...
a² = (2r)²+r²
a = √(5r²)
a = √(5)r units.
b = a-r
b = (√(5)r-r) units.
Considering similar triangle ratios.
Calculating r.
(√(5)r-r) = 2r
√(2) = r
Cross Multiply.
(√(5)r-r) = 2√(2)
r(√(5)-1)...
Let the base of the composite triangle be 1 unit.
a = 180-3-6
a = 171°
(1/sin171) = (b/sin3)
b = 0.33455515209 units.
c = 180-30-87
c = 180-117
c = 63°
(d/sin30) = (1/sin63)
d = 0.56116311882 un...
i = k
And i = 180-101-39 = 40°
Therefore;
k = 40°
While j = 101°
Or
Calculating i.
i = 90-11-39
i = 90+50
i = 40°
a = 180-2(11)
a = 180-22
a = 158°
b = 360-a
b = 360-158
b = 202°
Calculatin...
Considering similar triangle ratios.
3 = (3+x)
y = (4+y)
Where x and y are the width and length of the inscribed rectangle ascribing the red region respectively.
Cross Multiply.
12+3y = 3y+xy
xy...
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a = ½(180-150)
a = 15°
b = 90-15
b = 75°
(c/sin45) = (12/sin60)
c = 9.79795897113 cm.
(12/sin60) = (d/sin45)
d = 9.79795897113 cm.
e² = 9.79795897113²+12²-24*9.79795897113cos135
e = 20.1563111...
Let the side of the regular pentagon be 1 unit.
a = 108-90
a = 18°
b = 180-108-18
b = 54°
(1/sin54) = (c/sin108)
c = 1.17557050458 units.
(1/sin54) = (d/sin18)
d = 0.38196601125 un...
