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...
Let BC be 1 unit.
a = 180-30-18
a = 132°
a is angle BDC.
(1/sin132) = (b/ sin18)
b = 0.41582338164 units.
b is BD.
c = 180-72
c = 108°
c is angle BAC.
(1/sin108) = (d/sin36)
d = 0.61803398875 un...
Let alpha be x.
6x = 60
x = 10°
Alpha is 10°
Check accuracy.
x+x+2x+8x+6x = 18x
And x = 10
Therefore;
18x = 18*10 = 180° which is the sum of the interior angles of the ascribed t...
