Mathematics Question and Solution
Calculating x, side length of the regular pentagon.
a = ⅕(180(5-2))
a = ⅕(180*3)
a = 108°
a is the single interior angle of the regular pentagon.
b = ½(180-108)
b = 36°
c = 108-36
c = 72°
d = 45-36
d = 9°
e = 180-72-9
e = 180-81
e = 99°
f² = 2x²-2x²cos108
f² = 2x²+0.6180339887x²
f² = 2.6180339887x²
f = 1.6180339887x units.
It implies;
Observing Sine Rule.
(1.6180339887x/sin99) = (1/sin9)
1.6180339887xsin9 = sin99
x = sin99/(1.6180339887sin9)
x = 3.9021130327 units.
Or
(1/sin9) = (g/sin72)
g = 6.0795842914 units.
h = 72-45
h = 27°
(6.0795842914/sin72) = (i/sin27)
i = 2.9021130326 units.
It implies;
x = i+1
x = 2.9021130326+1
x = 3.9021130326 units.
