We know that the interior angles have to add to 180°, then we have that:
![\begin{gathered} C=180-69-32 \\ C=79 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/5bi3sjixwnomsqzeg477bydcdw4q22vym0.png)
Hence angle C=79°.
Now that we know the angle C we can use the law of sines to find a; the law of sines states that:
![(\sin A)/(a)=(\sin B)/(b)=(\sin C)/(c)](https://img.qammunity.org/2023/formulas/mathematics/college/dwc66mjebk1jvhqbzm1audqtmju1mnx2km.png)
From this we have the equation:
![(\sin A)/(a)=(\sin C)/(c)](https://img.qammunity.org/2023/formulas/mathematics/college/iiv9c3wulvhdllm8elt6212djghg05vpv2.png)
Plugging the values given and solving for a we have:
![\begin{gathered} (\sin32)/(a)=(\sin 79)/(5.7) \\ a=(5.7)(\sin 32)/(\sin 79) \\ a=3.08 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/n4hpvqe51loik0apucr9d7iit00o9o87ma.png)
Therefore a=3.08