Answer:
![\large\boxed{a=10.92\ and\ b=14.52}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7Ba%3D10.92%5C%20and%5C%20b%3D14.52%7D)
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:
![m\angle C+43^o+115^o=180^o](https://tex.z-dn.net/?f=m%5Cangle%20C%2B43%5Eo%2B115%5Eo%3D180%5Eo)
<em>subtract 158° from both sides</em>
![m\angle C=22^o](https://tex.z-dn.net/?f=m%5Cangle%20C%3D22%5Eo)
Step 2:
Use the law of sines to calculate the length a:
![\dfrac{6}{\sin22^o}=\dfrac{a}{\sin43^o}](https://tex.z-dn.net/?f=%5Cdfrac%7B6%7D%7B%5Csin22%5Eo%7D%3D%5Cdfrac%7Ba%7D%7B%5Csin43%5Eo%7D)
![\sin22^o\approx0.3746\\\\\sin43^o\approx0.6820](https://tex.z-dn.net/?f=%5Csin22%5Eo%5Capprox0.3746%5C%5C%5C%5C%5Csin43%5Eo%5Capprox0.6820)
<em>multiply both sides by 0.6820</em>
![a\approx10.92](https://tex.z-dn.net/?f=a%5Capprox10.92)
Step 3:
Use the law of sines to calculate the length b:
![\dfrac{6}{\sin22^o}=\dfrac{b}{\sin115^o}](https://tex.z-dn.net/?f=%5Cdfrac%7B6%7D%7B%5Csin22%5Eo%7D%3D%5Cdfrac%7Bb%7D%7B%5Csin115%5Eo%7D)
![\sin22^o\approx0.3746](https://tex.z-dn.net/?f=%5Csin22%5Eo%5Capprox0.3746)
To calculate sin115°, use the formula:
![\sin(180^o-\theta)=\sin\theta](https://tex.z-dn.net/?f=%5Csin%28180%5Eo-%5Ctheta%29%3D%5Csin%5Ctheta)
![\sin115^o=\sin(180^o-65^o)=\sin65^o](https://tex.z-dn.net/?f=%5Csin115%5Eo%3D%5Csin%28180%5Eo-65%5Eo%29%3D%5Csin65%5Eo)
![\sin65^o\approx0.9063](https://tex.z-dn.net/?f=%5Csin65%5Eo%5Capprox0.9063)
<em>multiply both sides by 0.9063</em>
![b\approx14.52](https://tex.z-dn.net/?f=b%5Capprox14.52)