Answer:
[tex]\begin{gathered} \alpha=\text{ 40\degree} \\ \beta=\text{ 70\degree} \\ a=68.4 \end{gathered}[/tex]Step-by-step explanation:
By the theorem of intern angles of a triangle, we know that the sum of all intern angles of a triangle must be 180°, therefore:
*There are two equal angles because there are two equal sides
[tex]\begin{gathered} \alpha=180-70-70 \\ \alpha=\text{ 40\degree} \\ \beta=\text{ 70\degree} \end{gathered}[/tex]Now, applying the law of sines, we can find side a. The law of sines is represented by the following equation:
[tex]\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}[/tex]Hence, if b=100, alpha=40° and betha=70°, solve for a:
[tex]\begin{gathered} \frac{a}{\sin (40)}=\frac{100}{\sin (70)} \\ a=\frac{100\cdot\sin (40)}{\sin (70)} \\ a=\text{ 68.4} \end{gathered}[/tex]
