Answer:
[tex]\large\boxed{a=10.92\ and\ b=14.52}[/tex]
Step-by-step explanation:
Step 1:
Calculate a measure of angle C.
We know: The sum of measures of angles in a triangle is equal 180°.
Therefore we have the equation:
[tex]m\angle C+43^o+115^o=180^o[/tex]
[tex]m\angle C+158^o=180^o[/tex] subtract 158° from both sides
[tex]m\angle C=22^o[/tex]
Step 2:
Use the law of sines to calculate the length a:
[tex]\dfrac{6}{\sin22^o}=\dfrac{a}{\sin43^o}[/tex]
[tex]\sin22^o\approx0.3746\\\\\sin43^o\approx0.6820[/tex]
[tex]\dfrac{6}{0.3746}=\dfrac{a}{0.6820}[/tex] multiply both sides by 0.6820
[tex]a\approx10.92[/tex]
Step 3:
Use the law of sines to calculate the length b:
[tex]\dfrac{6}{\sin22^o}=\dfrac{b}{\sin115^o}[/tex]
[tex]\sin22^o\approx0.3746[/tex]
To calculate sin115°, use the formula:
[tex]\sin(180^o-\theta)=\sin\theta[/tex]
[tex]\sin115^o=\sin(180^o-65^o)=\sin65^o[/tex]
[tex]\sin65^o\approx0.9063[/tex]
[tex]\dfrac{6}{0.3746}=\dfrac{b}{0.9063}[/tex] multiply both sides by 0.9063
[tex]b\approx14.52[/tex]
