Answer
B) 4.0 cm
Explanation
First, we can adapt the law of sines to the notation of our triangle:
![\frac{sin(W)}{w} =\frac{sin(U)}{u}](/tpl/images/0281/9022/baec1.png)
Now, we can infer from our diagram that
,
, and
, so we can replace the values in our previous expression:
![\frac{sin(W)}{w} =\frac{sin(U)}{u}](/tpl/images/0281/9022/baec1.png)
![\frac{sin(39)}{w} =\frac{sin(31)}{3.3}](/tpl/images/0281/9022/f8031.png)
Finally, we can solve for
:
![\frac{3.3sin(39)}{w} =sin(31)](/tpl/images/0281/9022/7744e.png)
![3.3sin(39)=wsin(31)](/tpl/images/0281/9022/cf361.png)
![\frac{3.3sin(39)}{sin(31)} =w](/tpl/images/0281/9022/3417e.png)
![w=\frac{3.3sin(39)}{sin(31)}](/tpl/images/0281/9022/5a257.png)
![w=4.03224](/tpl/images/0281/9022/d80cc.png)
Which rounds to ![w=4.0](/tpl/images/0281/9022/80b03.png)
We can conclude that the best approximation of w is 4.0 cm