Finding Diagonals in a Quadrilateral This is just a problem I came up with while reading one of my geometry textbooks:
If we have a quadrilateral with side lengths $a, b, c$ and $ d$ and we know the length of one of the diagonals to be $x$, what is the length of other diagonal in terms of $a, b, c, d$ and $x$?
I understand that there is only one possible length for the other diagonal and could prove this using SSS congruence, but I could not figure out how to derive the length of the other diagonal based on the provided info. Please help with this.

Since you know the length of one of the diagonals, as well as the lengths of all of the sides, you can use the law of cosines to compute all of the angles in the quadrilateral.
Having done this, you can use the law of cosines again to compute the length of the other diagonal.
