Answer:
w ≈ 4.0 cm
Step-by-step explanation:
We can find the approximation of the value of w by using the law of sines (which is given at the question). By applying the law to the question, we can come up with:
[tex]\boxed{\frac{sin\angle U}{|VW|}=\frac{sin\angle V}{|UW|} =\frac{sin\angle W}{|UV|} }[/tex]
Given:
- [tex]\angle U=31^o[/tex]
- [tex]\angle W=39^o[/tex]
- [tex]|VW|=3.3\ cm[/tex]
Therefore, to find w or |UV|, we use:
[tex]\begin{aligned}\frac{sin\angle U}{|VW|}&=\frac{sin\angle W}{|UV|}\\\\\frac{sin(31^o)}{3.3} &=\frac{sin(39^o)}{w} \\\\w&=\frac{sin(39^o)}{sin(31^o)} \times 3.3\\\\w&\approx\bf 4.0\ cm\end{aligned}[/tex]
