# How to calculate the length of line in a trapezium, given some other lines

It's best explained with an image of course:

L1, L2, h1 & h2 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 $L_3$.