First, we must find the dimension of the missing side, for this, we use the Pythagoras theorem
[tex]c^2=a^2+b^2[/tex]
Now, we replace these values an solve
[tex]\begin{gathered} (3\sqrt[]{3})^2=a^2+3^2 \\ a^2=(3\sqrt[]{3})^2-3^2 \\ a^2=(9\cdot3)-9 \\ a^2=27-9 \\ a^2=18 \\ a=\sqrt[]{18}=\sqrt[]{9\cdot2}=3\sqrt[]{2} \end{gathered}[/tex]
The magnitude of the missing side is
[tex]a=3\sqrt[]{2}[/tex]
Second, since we have all the sides defined we use the trigonometric tangent identity.
[tex]\tan (x)=\frac{O}{A}[/tex]
Where O is opposite and A is adjacent, now we can find tan A and B
Tan A
[tex]\tan (A)=\frac{3}{3\sqrt[]{3}}[/tex]
Tan B
[tex]\begin{gathered} \tan (B)=\frac{3\sqrt[]{2}}{3\sqrt[]{3}} \\ \tan (B)=\frac{\sqrt[]{2}}{\sqrt[]{3}} \end{gathered}[/tex]
