Mathematics Question and Solution
Notice.
Triangle ABC is isosceles.
Let BC be 1 unit.
It implies;
(1/sin24) = (a/sin(48+30))
a = 2.4048671724 units.
a is AB = AC.
b = 180-24-42-48
b = 180-114
b = 66°
b is angle ADB.
It implies;
(2.4048671724/sin66) = (c/sin(24+42))
c = 2.4048671724 units.
c is BD.
Notice.
Triangle ABD is also isosceles.
d² = 1²+2.4048671724²-2*1*2.4048671724cos30
d = 1.6180339888 units.
d is CD.
Therefore, the required angle, x is;
(1.6180339888/sin30) = (1/sinx)
x = 18°
