Answer:
[tex]AB=9.02\ units[/tex]
[tex]BC=7.45\ units[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
Remember that in a parallelogram opposites sides are parallel and congruent, opposites angles are congruent and consecutive angles are supplementary
step 1
Find the measure of angle ACB
we have
[tex]m\angle BAC=22^o[/tex] ----> given problem
[tex]m\angle ACB=m\angle DAC[/tex] ----> by alternate interior angles
[tex]m\angle DAC=27^o[/tex] ----> given problem
so
[tex]m\angle ACB=27^o[/tex]
step 2
Find the measure of angle ABC
The sum of the interior angles in any triangle must be equal to 180 degrees
In the triangle ABC of the figure
[tex]m\angle BAC+m\angle ACB+m\angle ABC=180^o[/tex]
substitute the given values
[tex]22^o+27^o+m\angle ABC=180^o[/tex]
[tex]49^o+m\angle ABC=180^o[/tex]
[tex]m\angle ABC=180^o-49^o[/tex]
[tex]m\angle ABC=131^o[/tex]
step 3
Find the length side AB
In the triangle ABC
Applying the law of sines
[tex]\frac{AC}{sin(ABC)}=\frac{AB}{sin(ACB)}[/tex]
substitute the given values
[tex]\frac{15}{sin(131^o)}=\frac{AB}{sin(27^o)}[/tex]
[tex]AB=\frac{15}{sin(131^o)}(sin(27^o))[/tex]
[tex]AB=9.02\ units[/tex]
step 4
Find the length side BC
In the triangle ABC
Applying the law of sines
[tex]\frac{AC}{sin(ABC)}=\frac{BC}{sin(BAC)}[/tex]
substitute the given values
[tex]\frac{15}{sin(131^o)}=\frac{BC}{sin(22^o)}[/tex]
[tex]BC=\frac{15}{sin(131^o)}(sin(22^o))[/tex]
[tex]BC=7.45\ units[/tex]
