Finding a diagonal of an arbitrary quadrangle knowing the other diag

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SUMMARY

To find the second diagonal of an arbitrary quadrangle when given the lengths of four sides and one diagonal, one can utilize the properties of triangles formed within the quadrangle. Specifically, by identifying triangles ACB and ACD, the angles CAB and CAD can be calculated, allowing for the determination of angle DAB. With two known sides and the included angle in triangle DAB, the second diagonal can be computed using the Law of Cosines.

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  • Understanding of triangle properties and the Law of Cosines
  • Knowledge of angle calculations in triangles
  • Familiarity with quadrilateral geometry
  • Basic trigonometric concepts
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  • Study the Law of Cosines for triangle calculations
  • Explore properties of quadrilaterals and their diagonals
  • Learn about angle sum properties in triangles
  • Investigate methods for solving complex geometric problems
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Mathematicians, geometry students, and anyone interested in solving problems related to quadrilaterals and triangle properties.

enricfemi
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for arbitrary quadrangle, if we know four side and one diagonal, can we know another diagonal? how?
 
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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. :smile:
 
though i found it almost impossible to find out the expression,it seems to be the only way to solve such complicated problem.

THX:smile:
 

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