Mathematics Question and Solution
Let BC = 1 unit.
(1/sin36) = (a/sin72)
a = 1.6180339887 units.
a is BD = CD.
b = 180-12-30
b = 138°
b is angle BAD.
(1.6180339887/sin138) = (c/sin30)
c = 1.2090569265 units.
c is AB.
d² = 1.2090569265²+1-2*1.2090569265cos84
d = 1.4862896509 units.
d is AC.
(1/sine) = (1.4862896509/sin84)
e = 42°
e is angle BAC.
f = b-e
f = 138-42
f = 96°
f is angle CAD.
Therefore, the required angle, angle ACD (x) is;
x = 180-30-36-f
x = 180-66-96
x = 180-162
x = 18°
