Let's construct a triangle, given two sides and a height (2 cases).





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

Note: The provided text is already in English, so no translation is needed for the second part. However, if you intended to translate the instruction itself, here it is:

Note: The provided text is already in English, so no translation is needed. However, if you intended to translate the instruction itself, it would be: "Translate the above text into English, please keep the original text's line breaks and format, and output the translation result directly."
Let $a$ and $b$ be the given two sides. Draw two parallel lines such that the distance between them is the given height.

First case. On one of the lines, we mark $a-\mathrm{t}, A B=a$ and from the midpoint $A$, we draw a circle with radius $b$. This circle intersects the other line at points $C$ and $C_{1}$. $A B C$ and $A B C_{1}$ are the sought triangles.

Second case. On one of the lines, we take an arbitrary point $A$ and from it, we draw circles with radii $a$ and $b$. These two circles intersect the other line at points $B, B_{1}$ and $C, C_{1}$. $A B C, A B C_{1}, A B_{1} C$ and $A B_{1} C_{1}$ are the sought triangles.

(Géza Alpár, Budapest, VI. district.)

Number of solutions: 31.