Let the square side length be a.
b² = 2a²
b = √(2)a units.
b is AC = BD, the diagonal of the square, ABCD.
c = x units.
d = (3-x) units.
Calculating x, observing similar plane shape (right-angle...
Notice!
The composite figure (plane shape) is not drawn to scale.
Let the side length of triangle ABC (equilateral triangle) be 1 unit.
1² = 2a²-2a²cos120
1 = 3a²
a = √(1/3)
a = ⅓√(3) units.
a is...
Let the radius of the inscribed circle be x.
a = (3-x) units.
b = 7-3
b = 4 units.
c = (7-x) units.
d = a+c
d = (3-x)+(7-x)
d = (10-2x) units.
Therefore, x (radius of the inscribe...
Notice!
The gray inscribed triangle is equilateral.
Calculating length x.
4² = 2a²-2a²cos120
16 = 3a²
a = √(16/3)
a = ⅓(4√(3)) units.
a = 2.3094010768 units.
a is the radius of the circle.
b² = 2...
Calculating length x.
5² = 8²+7²-2*8*7cosa
112cosa = 64+49-25
cosa = 88/112
a = acos(88/112)
a = 38.2132107017°
a is the angle opposite 5 units.
(5/sin38.2132107017) = (7/sinb)
b = 60°
b is the an...
Let the side length of the bigger regular pentagon be 1 unit.
a = ⅕*180(5-2)
a = 108°
a is the single interior angle of the regular pentagon.
b² = 2-2cos108
b = 1.6180339887 units.
c = 108-½(180-...
Let the bigger white semi circle's radius be a.
b = ½(a) units.
b is the radius of the smaller white circle.
c = a+b
c = a+½(a)
c = ½(3a) units.
c is the radius of the bigger white and gr...
Let the radius of the ascribed quarter circle be a.
It implies;
a² = 5²+b²
b = √(a²-25) units.
6² = b²+c²
c² = 36-b²
c = √(36-√(a²-25)²)
c = √(36-(a²-25))
c = √(61-a²) units.
d = 5+c
d = (5+√(61...
Calculating the required angle, x.
a = (√(3)-1) units.
Observing similar plane shape (right-angled triangle) side length ratios.
√(3) - 1
b - (√(3)-1)
Calculating b. Cross Multiply.
3-√(3) = b...
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/sin36.86989764584) =...
