Step 1
Find the missing angle taken as y
[tex]\begin{gathered} y+28+126=180\text{ (sum of angles in a triangle)} \\ y=180-28-126 \\ y=26^{\circ} \end{gathered}[/tex]
Step 2
State sine rule
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]
where;
[tex]\begin{gathered} a=8.2 \\ A=26^{\circ} \\ b=x \\ B=28^{\circ} \end{gathered}[/tex]
Step 3
Substitute and find the value of x
[tex]\begin{gathered} \frac{\sin26}{8.2}=\frac{\sin28}{x} \\ x\sin 26=8.2\sin 28 \\ \frac{x\sin26}{\sin26}=\frac{8.2\sin28}{\sin26} \\ x=8.781752273 \\ x\approx8.8\text{ to the nearest tenth} \end{gathered}[/tex]
Hence, x= 8.8 to the nearest tenth. Option C
