Since we are dealing with a right triangle, we can use the trigonometric identities shown below
[tex]\begin{gathered} cos\theta=\frac{A}{H},tan\theta=\frac{O}{A} \\ \theta\rightarrow\text{ interior angle} \\ O\rightarrow\text{ opposite side to}\theta \\ A\rightarrow\text{ adjacent side to}\theta \\ H\rightarrow\text{ hypotenuse} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} cosA=\frac{b}{c}\Rightarrow c=\frac{b}{cosA}=\frac{2}{cos(20\degree)}\approx2.13 \\ and \\ tanA=\frac{a}{b} \\ \Rightarrow a=btanA=2*tan(20\degree)\approx0.73 \end{gathered}[/tex]Finally, notice that angles A and B are complementary angles; thus
[tex]\begin{gathered} A+B=90\degree \\ \Rightarrow B=70\degree \end{gathered}[/tex]