Mathematics Question and Solution
Calculation Length CD.
a = 45+30
a = 75°
a is angle ECF.
b² = (4√(6))²+6²-2*6*4√(6)cos75
b = 10.0781555545 units.
b is EF.
c = ½(b)
c = ½(10.0781555545)
c = 5.03907777727 units.
It implies r, radius of the circle is;
sina = c/r
r = 5.03907777727/sin75
r = 5.21683719404 units.
Again, r is the radius of the circle.
d = 2(45)
d = 90°
e² = 2r²
e = √(2(5.21683719404)²)
e = 7.3777219125 units.
e is DF.
(7.3777219125/sin45) = (4√(6)/sinf)
f = 69.8960906392°
f is angle CDF.
g = 180-45-f
g = 135-69.8960906392
g = 65.1039093608°
g is angle CFD.
It implies, the required length CD, let it be x is;
(x/sin65.1039093608) = (7.3777219125/sin45)
x = 9.46410161511 units.
Again, x is length CD.
