Calculating Grey Area.
a² = 5²+2²
a = √(29) m.
tanb = 5/2
b = atan(5/2)°
c = (90+b)°
c = (90+atan(5/2))°
d² =√(29)²+4²-2*4√(29)cos(90+atan(5/2))
d = 9.2195444573 m.
d is the diagonal of the rect...
Let a be the side length of the purple inscribed square.
b² = 4
b = 2 cm.
b is the side length of the green inscribed square.
c² = 1
c = 1 cm.
c is the side length of the yellow ascribed square....
Calculating angle x.
Let AB be 1 unit.
a = 9-20
a = 70°
a is angle ABH.
b = 180-10-70
b = 100°
(c/sin70) = (1/sin100)
c = 0.9541888941 units.
(d/sin10) = (1/sin100)
d = 0.1763269807 units.
si...
Let BC be 1 unit.
a = ½(180-45)
a = ½(135)
a = 67.5°
a is angle ABC = angle ACB.
(1/sin45) = (b/sin67.5)
b = 1.3065629649 units.
b is AB.
c = 180-45-67.5
c = 67.5°
c is angle BEC....
Let the side length of the 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 = ½(180-108)
c = 36...
Notice!
Radius of the ascribed semi circle is 6 cm.
It implies;
Radius, a of the inscribed bigger circle is;
a = ½(6)
a = 3 cm.
Calculating b, radius of the smaller inscribed circle.
c = (6-b) c...
Calculating the area of the inscribed rectangle.
Let the length and width of the inscribed rectangle be x and y respectively.
Therefore, observing similar plane shapes (right-angled) side length ra...
Calculating area of the inscribed blue square.
Let the inscribed blue square side be x.
a² = 2x²
a = √(2)x units.
a is the diagonal of the inscribed blue square.
x² = 2b²
b² = x²/2
b = ½√(2)x uni...
Notice!
AQ = 6 cm.
a² = 6²+3²-2*6*3cos108
108° is the single interior angle of the regular pentagon.
a = 7.4916361229 cm.
a is AP.
cosb = 6/7.4916361229
b = acos(6/7.4916361229)°
b is angle PAQ....
(4+5+3)² = 2a²
a² = 72
a = 6√(2) cm.
a is the congruent adjacent sides of the right-angled triangle.
b² = √(72)²+3²-2*√(72)*3cos45
b² = 81-36
b = √(45)
b = 3√(5) cm.
(3√(5)/sin45) = (3/sinc)
c = 1...
