Mathematics Question and Solution
Let the side length of the regular pentagon be 2 units.
Therefore;
Arc radius is;
= 2 units.
Calculating Circle Radius.
a = 180(3)/5
a =108°
b = ½(180-108)
b = 36°
c = 108-36
c =72°
cos72 = 1/d
d = 3.2360679775 units.
e = 90-72
e = 18°
f = 27-18
f =9°
sin27 = g/h
h = g/sin27
h = 2.2026892646g units.
Where g is the radius of the inscribed circle.
It implies;
(2+g)² = (2.2026892646g)²+3.2360679775²-2*3.2360679775*2.2026892646gcos9
4+4g+g² = 4.8518399964g²+10.472135955-14.0805880855g
3.8518399964g²-18.0805880855g+6.472135955 = 0
Solving the above quadratic equation.
g = 0.390436 units.
Where g is radius of the circle.
It implies;
Radius Circle ÷ Radius Arc to 2 decimal places is;
0.390436÷2
= 0.195218
≈ 0.20
