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$L1$, $L2$, $h_1$ & $h_2$ are all given, and I would like to calculate the length of $L3$. Is it possible, and how?

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Denote the angle of the triangle by $\alpha$. Express all segments of the hypotenuse using $\alpha$ and $h_2,L_1,L_2$, then write an equation for $\alpha$ using $h_1$. Solve for $\alpha$, and find $L_3$.

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