Statement Problem: Solve for the missing sides of the triangle;
Solution:
The sum of angles in a triangle is 180degrees. Thus,
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^o \\ \angle B=180^o-\angle A-\angle C \\ \angle B=180^o-42^o-96^o \\ \angle B=42^o \end{gathered}[/tex]
Since measure angle A and measure angle B are equal. Thus, the triangle is isosceles and the two sides are equal.
[tex]a=b[/tex]
We would apply sine rule to find the missing side a.
[tex]\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} \\ \frac{\sin A}{a}=\frac{\sin C}{c} \end{gathered}[/tex][tex]\begin{gathered} \frac{\sin42^o}{a}=\frac{\sin96^o}{12} \\ a=\frac{12\sin42^o}{\sin96^o} \\ a=8.07 \\ a\approx8.1 \end{gathered}[/tex]
Thus,
[tex]a=b=8.1[/tex]
CORRECT ANSWERS:
[tex]\begin{gathered} a=8.1 \\ b=8.1 \\ m\angle B=42^o \end{gathered}[/tex]
