Mathematics Question and Solution
Let AC be 1 unit.
a = 180-12-15
a = 153°
a is angle ADC.
Observing Sine Rule.
(1/sin153) = (b/sin12)
b = 0.4579648493 units.
b is CD.
c = 180-12-18-15-33
c = 180-78
c = 102°
c is angle ABC (angle x + angle y).
d = 18+12
d = 30°
d is angle BAC.
Observing Sine Rule.
(1/sin102) = (e/sin30)
e = 0.5111702974 units.
e is BC.
Observing Cosine Rule.
f² = 0.5111702974²+0.4579648493²-2*0.5111702974*0.4579648493cos33
f = 0.2799368207 units.
f is BD.
Therefore, Calculating y Observing Sine Rule.
(0.2799368207/sin33) = (0.4579648493/siny)
y = 63°
It implies;
x+y = c (angle ABC)
x+63 = 102
x = 102-63
x = 39°
Therefore;
Angle x = 39°
Angle y = 63°
