Mathematics Question and Solution
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(⅓(4√(3)))²-2(⅓(4√(3)))²cos60
b = 2.3094010768 units.
tanc = 1/2.3094010768
c = atan(1/2.3094010768)
c = 23.413224446°
sin23.413224446 = 1/d
d = 2.5166114785 units.
e = 60-c
e = 60-23.413224446
e = 36.586775554°
cos36.586775554 = 2.3094010768/f
f = 2.876127404 units.
It implies, x, the required length is;
x² = 2.876127404²+2.5166114785²-2*2.876127404*2.5166114785cos60
x = 2.7142857144 units.
