First, we calculate the measure of angle A. We know that the sum of the internal angles of a triangle is 180°. Then:
[tex]\begin{gathered} 45°+70°+\angle A=180° \\ 115\degree+\angle A=180\degree \\ \\ \Rightarrow\angle A=65\degree \end{gathered}[/tex]
Finally, using the law of Sines:
[tex]\begin{gathered} \frac{BC}{\sin A}=\frac{AC}{\sin B}=\frac{AB}{\sin C} \\ \\ \Rightarrow\frac{BC}{\sin65\degree}=\frac{15}{\sin70\degree}=\frac{AB}{\sin45\degree} \\ \\ \therefore BC=14.5 \\ \therefore AB=11.3 \end{gathered}[/tex]
