Mathematics Question and Solution
sin36 = c/b
c = bsin36 units.
c = 0.5877852523b units.
Calculating b.
b² = (0.5877852523b)²+(0.5(b+1))²
0.6545084972b² = ¼(b²+2b+1)
1.6180339888b²-2b-1 = 0
It implies;
b = 1.61803 units.
Therefore;
a = b+1
And b = 1.61803 units.
a = 1.61803+1
a = 2.61803 units.
cos72 = d/1.61803
d = 0.4999987674 units.
sin72 = e/1.61803
e = 1.5388379751 units.
f = 2.61803+1.5388379751
f = 4.1568679751 units.
g = 1.61803+0.4999987674
g = 2.1180287674 units.
tanh = 4.1568679751/2.1180287674
h = 63°
j = 180-2*63
j = 180-126
j = 54°
k = 2j
k = 2*54
k = 108°
l = ½(180-108)
l = 36°
cos36 = (0.5*1.61803)/m
m = 0.9999975348 units.
m = 1 unit.
m is the radius of the circle.
Therefore, area circle is;
πr²
And r = m = 1 unit.
= π(1)²
= π square units.
