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#1 2010-07-28 23:30:37

yehoram
Member
Registered: 2010-06-24
Posts: 8

Obtuse angle triangle

Abc triangle given:
ac = t
ab = 2t
bc = Kt
Find the values of k for the triangle to be obtuse angle ???

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#2 2010-07-28 23:37:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Obtuse angle triangle

Hi yehoram;

Do you have a drawing? Capitals are angles and small letters are sides? Your question states triangle Abc, you mean abc?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2010-07-28 23:44:27

yehoram
Member
Registered: 2010-06-24
Posts: 8

Re: Obtuse angle triangle

No , sorry !

abc triangle given:
let ac = t
and ab = 2t
and bc = Kt

Find the values of k for the triangle to be obtuse angle ???

Last edited by yehoram (2010-07-28 23:44:55)

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#4 2010-07-28 23:46:55

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Obtuse angle triangle

Okay those are your sides!


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#5 2010-07-28 23:57:03

Anakin
Member
Registered: 2009-10-04
Posts: 145

Re: Obtuse angle triangle

A guess here, for all k values greater than √5 and less than 3.

That's assuming that t is just a constant (meaning side ac is half as long as side ab). So I just set t=1.

@Bobby, I used the cosine law too and it somehow worked out. I used k^2 = 1^2+2^2 - 2(1*2)cos(x).

(k^2 - 5)/(-4) > -1 and we get -3 < k < 3 but k cannot be negative.
(k^2 - 5)/(-4) > 0 and we get -√5 < k < √5 but once again k cannot be negative.

So I came up with k values greater than √5 and less than 3.

Not entirely sure if that is correct.

Last edited by Anakin (2010-07-29 00:20:00)

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#6 2010-07-29 00:08:56

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Obtuse angle triangle

Hi Anakin;

I am making a big mess here with the law of cosines, what are you trying? I am trying to get one angle between 90 and 180 degrees.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#7 2010-07-29 00:24:55

Anakin
Member
Registered: 2009-10-04
Posts: 145

Re: Obtuse angle triangle

Does that seem correct?

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#8 2010-07-29 00:25:17

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Obtuse angle triangle

Hi Anakin;

Looks like you are assuming that k*t is on the left, I am getting some answers with 2 t on the left


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#9 2010-07-29 00:31:26

Anakin
Member
Registered: 2009-10-04
Posts: 145

Re: Obtuse angle triangle

What do you mean on the left? I figured the only angle that could be obtuse in this triangle is the one across from side bc.

This is what I saw it as:

http://i32.tinypic.com/33ljxoy.png

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#10 2010-07-29 00:32:13

yehoram
Member
Registered: 2010-06-24
Posts: 8

Re: Obtuse angle triangle

I think is go like this

Last edited by yehoram (2010-07-29 00:34:42)

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#11 2010-07-29 00:40:42

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Obtuse angle triangle

Hi;

I am getting the interval ( - 1 , 3 ) for the second one with ( 2 t )^2 on the left


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#12 2010-07-29 00:42:12

yehoram
Member
Registered: 2010-06-24
Posts: 8

Re: Obtuse angle triangle

The answer is :

Last edited by yehoram (2010-07-29 00:42:43)

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#13 2010-07-29 00:43:55

Anakin
Member
Registered: 2009-10-04
Posts: 145

Re: Obtuse angle triangle

Well, can't we get rid of the t's if they are simply just constants?

So that means
ac = 1
ab = 2
bc = k

Since ONLY the angle across from side bc can be obtuse in this triangle, it would be the reason why we have k^2 on the left side of the equation.

So k^2=1^2+2^2 - 2(1*2) cos (x). For that matter, I think we could simply let t equal a random number like 2 or 4 and it still turns out to be correct.

I still don't see how it could be the second part Yehoram. Because if you say that 1 < k < 3, then that means k can be a number such as 1.1; and that would mean that not a single obtuse angle exists if the three sides are 1.1, 1 and 2.

I believe only the first part of your answer is correct.

Last edited by Anakin (2010-07-29 00:47:21)

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#14 2010-07-29 00:47:46

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Obtuse angle triangle

Hi;

For:

( 2 t ) ^2 = 1 + k^2 + 2k * cos(x)

I am getting the open interval ( -√ 3 , 3 ).

Anakin;

I f we are sure it does not equal zero. We can divide through by t.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#15 2010-07-29 00:51:43

Anakin
Member
Registered: 2009-10-04
Posts: 145

Re: Obtuse angle triangle

But since none of the sides are of zero length, then we can indeed divide by t.

And Bobby, I THINK (I have to be cautious about being wrong lol) the reason why you cannot have 2t^2 on the left side of the equation is because the angle across of it is not the obtuse angle that we are looking for. Only the angle across from (kt)^2 can be obtuse, that is why I put it on the left side.

Last edited by Anakin (2010-07-29 00:52:37)

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#16 2010-07-29 00:53:24

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Obtuse angle triangle

Hi Anakin;

Why is that, what is wrong with his diagram that I am missing?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#17 2010-07-29 01:01:33

Anakin
Member
Registered: 2009-10-04
Posts: 145

Re: Obtuse angle triangle

Perhaps I was wrong.

I drew it out, I guess you were right. Then I suppose there is a set of answers depending on which angle is obtuse?

Last edited by Anakin (2010-07-29 01:05:22)

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#18 2010-07-29 01:04:29

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Obtuse angle triangle

Hi Anakin;

In post #10 it does look scaled correctly. I think you are assuming that k t is larger than 2t. That is not necessarily true.  Another idea is that I am a dummy.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#19 2010-07-29 01:06:27

Anakin
Member
Registered: 2009-10-04
Posts: 145

Re: Obtuse angle triangle

No dummy here. Like always, you were right. smile

However, you said -√3  < x < 3. It cannot be negative, no?

Last edited by Anakin (2010-07-29 01:10:01)

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#20 2010-07-29 01:08:22

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Obtuse angle triangle

Why don't we have the same answers he has in post #12?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#21 2010-07-29 01:10:26

Anakin
Member
Registered: 2009-10-04
Posts: 145

Re: Obtuse angle triangle

Is it because in your equation ( 2 t ) ^2 = 1 + k^2 + 2k * cos(x), should that not be a negative sign before the 2k?

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#22 2010-07-29 01:13:17

soroban
Member
Registered: 2007-03-09
Posts: 452

Re: Obtuse angle triangle



    A *
      *   *    t
   2t *       *
      *           *
    B *   *   *   *   * C
             kt




    C *
      *   *    kt
    t *       *
      *           *
    A *   *   *   *   * B
             2t

. .


. .




    A *
      *   *    2t
    t *       *
      *           *
    C *   *   *   *   * B
             kt

. .


. .


.

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#23 2010-07-29 01:15:21

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Obtuse angle triangle

God! I told you I was a dummy!

The answer I get now is the open interval ( -3 ,  √ 3  )

Okay so we can't have a side that is minus or a side where that is zero.. So now I see it.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#24 2010-07-29 01:21:28

Anakin
Member
Registered: 2009-10-04
Posts: 145

Re: Obtuse angle triangle

Working with your equation: I solved the inequality -1<(3-k^2)/(-2k)<0 and I get:

-3 < k < -√3
1 < k < √3

The first one cannot be accepted so therefore, the second is correct.

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#25 2010-07-29 01:25:06

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Obtuse angle triangle

Yes, I see that no negative or zero sides of course. Forgot to prune out the impossible cases, Like you and soroban did.

Also hurriedly solved the inequality by plugging in -1 and 0, to get a fast answer but that produced extra solutions. So all in all a pretty bad performance.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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