Mathematics Question and Solution
Calculating x, length CD.
4² = 6²+6²-2*6*6cosa
72cosa = 72-16
cosa = 56/72
a = acos(7/9)
a = 38.942441269°
a is angle ABC.
b = ½(180-a)
b = 70.5287793655°
b is angle ADB = angle BAD.
2c = 180-b
2c = 109.4712206345
2c is 2 alpha, angle ADC.
c = 54.7356103172°
c is alpha, angle CAD.
d = 180-2c-c
d = 180-109.4712206345-54.7356103172
d = 15.7931690484°
d is angle ACB.
Therefore, x, length CD is;
(x/sin54.7356103172) = (4/sin15.7931690484)
x = 12 units.
Again, x is length CD.
