Mathematics Question and Solution
Let the side length of the regular heptagon be 1 unit.
a = ⅐(180(7-2))
a = 128.5714285714°
Where a is the single interior angle of the regular heptagon.
b² = 2-2cos128.5714285714
b = 1.8019377358 units.
c = ½(180-128.5714285714)
c = 25.7142857143°
d = 128.5714285714-25.7142857143
d = 102.8571428571°
e² = 1.8019377358²+1-2*1.8019377358cos102.8571428571
e = 2.2469796037 units.
Where e is r+q+p.
(2.2469796037/sin102.8571428571) = (1/sinf)
f = 25.7142857144°
g = 180-25.7142857144-102.8571428571
g = 51.4285714285°
h = (180-2*51.4285714285)
h = 77.142857143°
Calculating p.
p² = 2-2cos77.142857143
p = 1.2469796037 units.
It implies;
r+q = 2.2469796037-p
r+q = 2.2469796037-1.2469796037
r+q = 1 units.
s = 180-2*((900/7)-51.4285714285
s = 25.7142857141°
Calculating r.
r² = 2-2cos25.7142857141
r = 0.4450418679 units.
It implies.
q = 1-r
q = 1-0.4450418679
q = 0.5549581321 units.
Therefore;
(p/q) - (q/r) is;
= (1.2469796037/0.5549581321) - (0.5549581321/0.4450418679)
= 2.2469796036-1.2469796038
= 1
