Mathematics Question and Solution
Let a be 1 unit.
e = ½(180-45)
e = 67.5°
tane = 1/f
f = 1/tan(67.5)
f = 0.41421356237 units
g = 1-f
g = 1-0.41421356237
g = 0.58578643763 units.
2h² = a²
2h² = 1
h = ½√(2) units.
h = 0.70710678119 units.
j = 45-(90-67.5)
j = 45-22.5
j = 22.5°
Therefore, calculating lengths b, c and d.
Length b is;
b = √(1²+0.58578643763²)
b = 1.15894165104 units.
Length c is;
c = √(1²+0.41421356237²)
c = 1.08239220029 units.
Length d is;
d² = 1.08239220029²+0.70710678119²-2*1.08239220029*0.70710678119cos22.5
d = 0.50730593617 units.
It implies;
(b²+c²)÷(a²+d²) is;
(1.15894165104²+1.08239220029²)÷(1²+0.50730593617²)
= 2
