Let's construct a triangle, given one side and two heights (2 cases).





Translate the above text into English, please keep the original text's line breaks and format, and output the translation result directly. 

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(1.) Given: $A B, A A_{1}, B B_{1}$.

From $A$ and $B$, we draw arcs with radii $A A_{1}$ and $B B_{1}$, respectively, and construct tangents to these arcs from $B$ and $A$, respectively. The tangents intersect at the third vertex, $C$.

(2.) Given: $A B, B B_{1}, C C_{1}$.

From $B$, we draw a circle with radius $B B_{1}$, to which we construct a tangent from $A$; this tangent intersects at the point $C$, the sought vertex, with the line parallel to $A B$ and at a distance $C C_{1}$ from it.

(Harsányi Zoltán, Eger.)

Number of solutions: 30.