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Sagot :
we know that
A=42 degrees
B=67 degrees
a=15 units
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
42+67+C=180
C=180-109
C=71 degrees
step 2
Find out the measure of the side b
Applying the law of sines
[tex]\frac{a}{sinA}=\frac{b}{sinB}[/tex]substitute given values
[tex]\begin{gathered} \frac{15}{s\imaginaryI n42^o}=\frac{b}{s\imaginaryI n67^o} \\ \\ b=\frac{15*s\mathrm{i}n67^o}{s\imaginaryI n42^o} \\ \\ b=20.6\text{ units} \end{gathered}[/tex]step 3
Find out the measure of the side c
Applying the law of sines
[tex]\frac{a}{sinA}=\frac{c}{sinC}[/tex]substitute given values
[tex]\begin{gathered} \frac{15}{s\imaginaryI n42^o}=\frac{c}{s\imaginaryI n71^o} \\ \\ c=\frac{15*s\mathrm{i}n71^o}{s\imaginaryI n42^o} \\ \\ c=21.2\text{ units} \end{gathered}[/tex]
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