Answer
B) 4.0 cm
Explanation
First, we can adapt the law of sines to the notation of our triangle:
[tex]\frac{sin(W)}{w} =\frac{sin(U)}{u}[/tex]
Now, we can infer from our diagram that [tex]W=39[/tex], [tex]U=31[/tex], and [tex]u=3.3[/tex], so we can replace the values in our previous expression:
[tex]\frac{sin(W)}{w} =\frac{sin(U)}{u}[/tex]
[tex]\frac{sin(39)}{w} =\frac{sin(31)}{3.3}[/tex]
Finally, we can solve for [tex]w[/tex]:
[tex]\frac{3.3sin(39)}{w} =sin(31)[/tex]
[tex]3.3sin(39)=wsin(31)[/tex]
[tex]\frac{3.3sin(39)}{sin(31)} =w[/tex]
[tex]w=\frac{3.3sin(39)}{sin(31)}[/tex]
[tex]w=4.03224[/tex]
Which rounds to [tex]w=4.0[/tex]
We can conclude that the best approximation of w is 4.0 cm
