Given are two sides of a triangle and the median to the third side. The triangle needs to be constructed and the third side needs to be calculated.





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Let the sides $a$ and $b$ and the median $s$ be given. If $D$ is the midpoint of $A C$ and $E$ is the midpoint of $A B$, then all sides of the triangle $C D E$ are known.

$C E=s, D E=a / 2, C D=b / 2$, and thus it can be constructed. Extending $C D$ by $D A=C D$ gives $A$, and extending $A E$ by $B E=A E$ gives $B$.

The condition for constructibility: $(a-b) / 2<s<(a+b) / 2$