Mathematics Question and Solution
Calculating x.
a² = 1²+1²
a² = 2
a = √(2) units.
b = ⅛*180(8-2)
b = ⅛*180*6
b = 135°
b is the single interior angle of a regular octagon with side length √(2) units. Half the regular octagon is derived to inscribe the ascribed half circle.
c² = 2a²-2a²cos135
c² = 2√(2)²-2√(2)²cos135
c = 2.61312592975 units.
Let r be the radius of the ascribed half circle.
r²+r² = c²
2r² = 2.61312592975²
r = √(2.61312592975²/2)
r = 1.84775906502 units.
d²+d² = r²
2d² = 1.84775906502²
d = 1.30656296487 units.
d is the radius of the inscribed green half circle.
e = 2d
e = 2.61312592975 units.
e is the diameter of the inscribed green half circle.
It implies, x is;
e² = 1²+x²
x² = 2.61312592975²-1²
x = √(5.82842712473)
x = 2.41421356237 units.
x = (1+√(2)) units.
