Mathematics Question and Solution
Let BC be 1 unit.
a = 180-57-49-33
a = 180-139
a = 41°
a is angle BDC.
Observing Sine Rule.
(1/sin41) = (b/sin(49+33))
b = 1.5094191604 units.
b is BD.
c = 180-33-30-41
c = 180-104
c = 76°
c is angle CAD.
Observing Sine Rule.
(1/sin41) = (d/sin57)
d = 1.2783462019 units.
d is CD.
Observing Sine Rule.
(1.2783462019/sin76) = (e/sin33)
e = 0.7175515907 units.
e is AD.
Observing Cosine Rule.
f² = 0.7175515907²+1.5094191604-2*0.7175515907*1.5094191604cos30
f = 0.9577402043 units.
f is AB.
Therefore, the required angle is;
Let it be g.
Calculating g, Observing Sine Rule.
(0.9577402043/sin30) = (0.7175515907/sing)
g = 22°
It implies, the required angle, g, angle ABD is 22°
