we know that
A=110 degrees
B =27 degrees
c=6
step 1
Find out the measure of angle C
Remember that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
A+B+C=180 degrees
substitute given values
110+27+C=180
137+C=180
C=180-137
C=43 degrees
step 2
Find out the length side a
Applying the law of sines
[tex]\frac{c}{sinC}=\frac{a}{sinA}[/tex]
substitute given values
[tex]\frac{6}{s\imaginaryI n43^o}=\frac{a}{s\imaginaryI n110^o}[/tex]
solve for a
[tex]\begin{gathered} a=\frac{6*s\mathrm{i}n110^o}{s\imaginaryI n43^o} \\ a=8.3\text{ units} \end{gathered}[/tex]
step 3
Find out the length of side b
Apply the law of sines
[tex]\frac{c}{s\imaginaryI nC}=\frac{a}{s\imaginaryI nA}[/tex]
substitute given values
[tex]\frac{6}{s\imaginaryI n43^o}=\frac{b}{s\imaginaryI n27^o}[/tex]
solve for b
[tex]\begin{gathered} b=\frac{6*s\mathrm{i}n27^o}{s\imaginaryI n43^o} \\ b=4.0\text{ units} \end{gathered}[/tex]
