- #1
enricfemi
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for arbitrary quadrangle, if we know four side and one diagonal, can we know another diagonal? how?
Finding a diagonal of an arbitrary quadrangle knowing the other diag
- Thread starter enricfemi
- Start date
In summary, if we know four sides and one diagonal of an arbitrary quadrangle, we can find the other diagonal by using the formulas for sides-and-angles of a triangle. By breaking the quadrangle into two triangles, we can find the angles and use them to find the missing diagonal. This may seem like a difficult task, but it is the only way to solve such a complicated problem. Thank you for your help!
- #2
tiny-tim
Science Advisor
Homework Helper
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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.
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.
- #3
enricfemi
- 195
- 0
though i found it almost impossible to find out the expression,it seems to be the only way to solve such complicated problem.
THX:rofl:
THX:rofl:
1. How do you find the diagonal of an arbitrary quadrangle?
The diagonal of an arbitrary quadrangle can be found by using the Pythagorean theorem. First, determine the length of both diagonals of the quadrangle. Then, use the formula c² = a² + b², where c represents the length of the diagonal and a and b represent the lengths of the other two sides of the quadrangle. Finally, solve for c to find the length of the diagonal.
2. What is an arbitrary quadrangle?
An arbitrary quadrangle is a four-sided polygon with no specific properties or restrictions. It can have any shape, size, or orientation, as long as it has four sides and four angles.
3. Can the diagonal of an arbitrary quadrangle be found without knowing the lengths of the other two diagonals?
No, the diagonal of an arbitrary quadrangle cannot be found without knowing the lengths of the other two diagonals. The Pythagorean theorem requires the lengths of all three sides of a right triangle to solve for the missing length.
4. Are there any other methods for finding the diagonal of an arbitrary quadrangle?
Yes, there are other methods for finding the diagonal of an arbitrary quadrangle, such as using trigonometric ratios or the law of cosines. However, the Pythagorean theorem is the simplest and most commonly used method.
5. Is it possible for an arbitrary quadrangle to not have a diagonal?
No, it is not possible for an arbitrary quadrangle to not have a diagonal. Every quadrangle, by definition, has four sides and four angles, and therefore must have at least two diagonals connecting opposite corners.
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