Finding a diagonal of an arbitrary quadrangle knowing the other diag

[enricfemi]

for arbitrary quadrangle, if we know four side and one diagonal, can we know another diagonal? how?

 

[tiny-tim]

Hi!

Do you know the formulas for sides-and-angles of a triangle?

If so, you have two triangles, ACB and ACD, say, so you can find all the angles.

In particular, you can find angles CAB and CAD.

Add them to get angle DAB.

Now you have a triangle DAB of which you know two sides and the angle in between.

 

[enricfemi]

though i found it almost impossible to find out the expression,it seems to be the only way to solve such complicated problem.

THX