Can you illustrate the text about angles?
Solution 1:
In the image above, say you started with triangle $ABC$, you know $\angle CAB$. You also know $AC$ and $BC$. If you start from the segment $AC=A'C'$, and the angle $CAB=\angle C'A'B'$, at the distance $C'B'=CB$ there are two points (see $B$ and $D$ in the figure. Is this explanation enough?