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# One of the inside angles of a parallelogram is 60 degrees.

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Director
Joined: 17 Oct 2005
Posts: 877
One of the inside angles of a parallelogram is 60 degrees.  [#permalink]

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22 Feb 2006, 00:50
One of the inside angles of a parallelogram is 60 degrees. What is the ratio of the length of the two diagonals?

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Intern
Joined: 16 Aug 2005
Posts: 37

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22 Feb 2006, 05:01
mama: Don't we need another assumption on the length of the sides of the parallelogram ?
Director
Joined: 17 Oct 2005
Posts: 877

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22 Feb 2006, 15:59
I really dont know if the q. is missing something. How did you guys arrive at your answers?

the oa i have is sin(30)/sin(60)=1/sqrt(3)
Intern
Joined: 16 Aug 2005
Posts: 37

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22 Feb 2006, 23:48
Right the question is missing that the sides of the parallelogram are of equal length L.
Then we have the length of shortest diagonal is L (equilateral triangle) and the length of the other diagonal is 2*sin(60)*L=sqr(3)*L.
Director
Joined: 17 Oct 2005
Posts: 877

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23 Feb 2006, 00:12
pete, can you be more elaborate? what is the inside angle? I am picturing a figure with four angles, 60-120-60-120. there are two diagonals and the intersection between them cuts the diagonal in half. am i right? thanks.
CEO
Joined: 20 Nov 2005
Posts: 2774
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008

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23 Feb 2006, 00:32
1
I don't see anything missing.

In the attached figure.

Say sides of ||gram are x and y.

We know that and lets say angle ADC = 60 Then

DCB = 120 and ABC = 60

So angle EDC = 30 and DCE = 60 and DEC = 90. Which mean the diagnols are bisecting at right angles. This happens only in case of rhombus, which is special ||gram having all sides equal.

Now we just have to find the ratio of sides of a right angle triangle whose other angles are 30, 60.

This leads to the solution sin(30)/sin(60)=1/sqrt(3)
Attachments

PGram.JPG [ 5.97 KiB | Viewed 4646 times ]

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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Director
Joined: 17 Dec 2005
Posts: 532
Location: Germany

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23 Feb 2006, 01:27
@ps dahiya

You suppose that the diagonals divide the respective angles exactly in two equal angles, but that is just the case in special cases, naemly when the figure is a square or a rhombus.

"So angle EDC = 30 and DCE = 60 and DEC = 90. Which mean the diagnols are bisecting at right angles. This happens only in case of rhombus, which is special ||gram having all sides equal.

Now we just have to find the ratio of sides of a right angle triangle whose other angles are 30, 60.

This leads to the solution sin(30)/sin(60)=1/sqrt(3)" is a circular argument
Intern
Joined: 16 Aug 2005
Posts: 37

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23 Feb 2006, 02:03
ps_dahiya wrote:
So angle EDC = 30 and DCE = 60 and DEC = 90. Which mean the diagnols are bisecting at right angles.

How do you get EDC=30 ??
CEO
Joined: 20 Nov 2005
Posts: 2774
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008

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23 Feb 2006, 02:34
@ps dahiya

You suppose that the diagonals divide the respective angles exactly in two equal angles, but that is just the case in special cases, naemly when the figure is a square or a rhombus.

"So angle EDC = 30 and DCE = 60 and DEC = 90. Which mean the diagnols are bisecting at right angles. This happens only in case of rhombus, which is special ||gram having all sides equal.

Now we just have to find the ratio of sides of a right angle triangle whose other angles are 30, 60.

This leads to the solution sin(30)/sin(60)=1/sqrt(3)" is a circular argument

What am I doing. I think I should sleep now.
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Non-Human User
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Posts: 9460
Re: One of the inside angles of a parallelogram is 60 degrees.  [#permalink]

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05 Mar 2018, 07:38
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Re: One of the inside angles of a parallelogram is 60 degrees. &nbs [#permalink] 05 Mar 2018, 07:38
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