Mathematics Question and Solution
3² = 2c²-2c²cos108
108° is the single interior angle of the regular pentagon.
It implies;
9 = 2.6180339887c²
c² = 3.4376941013
c = 1.8541019663 units.
c is the side length of the regular pentagon.
sin36 = d/c
d = 1.8541019663sin36
d = 1.089813792 units.
cos36 = e/c
e = 1.8541019663cos36
e = 1.5 units.
f = 1.5-1
f = 0.5 units.
tang = f/d
tang = 0.5/1.089813792
g = atan(0.5/1.089813792)
g = 24.6453719079°
h = 54-g
h = 29.3546280921°
j = 180-108-h
j = 42.6453719079°
It implies;
Calculating a.
(a/sin29.3546280921) = (1.8541019663/sin42.6453719079)
a = 1.3416407865 units.
Notice!
a+b = c
1.3416407865+b = 1.8541019663
b = 1.8541019663-1.3416407865
b = 0.5124611798 units.
It implies;
a:b is;
1.3416407865:0.5124611798
= 1.3416407865÷0.5124611798
= 2.6180339886
≈ 2.62 to 2 decimal places.
