Answer:
7.8 units
Step-by-step explanation:
Given: In ΔPQR, m∠P = 33, m∠Q = 82, and PR = 14.2.
Law of sine:
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin b}=\dfrac{c}{\sin C}[/tex]
Using law of sine, we get
[tex]\dfrac{QR}{\sin P}=\dfrac{PR}{\sin Q}[/tex]
[tex]\dfrac{QR}{\sin (33)}=\dfrac{14.2}{\sin (82)}[/tex]
[tex]\frac{QR}{0.544639}=\frac{14.2}{0.990268}[/tex]
[tex]QR=\frac{14.2}{0.990268}\times 0.544639[/tex]
[tex]QR=7.809879[/tex]
[tex]QR\approx 7.8[/tex]
Therefore, the length of QR is 7.8 units.
