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#1 2015-04-09 20:07:17

hussam
Member
Registered: 2015-04-06
Posts: 46

kind of the triangle

Hi;

1. A triangle ABC
The angles achieve the following relationship :Sin(A)=Sin(B).Cos(C)
what kind of this triangle?

2. A triangle ABC
The angles achieve the following relationship : [Sin(A/2)]^2=Cos(B).Cos(C)
what kind of this triangle?

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#2 2015-04-09 23:07:01

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,138

Re: kind of the triangle

hi hussam,


Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#3 2015-04-10 03:31:48

hussam
Member
Registered: 2015-04-06
Posts: 46

Re: kind of the triangle

hi bob ;

Excellent! q2 is correct


Q1. the method that i know

sin(A)=sin(B).cos(C)

so: sin(B+C)=sin(B).cos(C)

sin(B).cos(C) + cos(B). sin(C)= sin(B).cos(C)

==>  cos(B). sin(C)=0

Either :  sin(C)=0    =>   C=0    ( Rejected,because (C)is an angle in the triangle)   

or :     cos(B)=0    =>   B= π/2 rad   

thus,it is a right triangle .

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#4 2015-04-10 04:00:55

hussam
Member
Registered: 2015-04-06
Posts: 46

Re: kind of the triangle

3.  A triangle ABC
The angles achieve the following relationship :Sin(B).Cos(B)=Sin(C).Cos(C)
what kind of this triangle?

Last edited by hussam (2015-04-10 04:01:48)

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#5 2015-04-10 04:15:20

hussam
Member
Registered: 2015-04-06
Posts: 46

Re: kind of the triangle

4.   A triangle ABC
The angles achieve the following relationship :Sin(2A)+sin(2B)=2Sin(C)
what kind of this triangle?

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#6 2015-04-10 05:19:14

hussam
Member
Registered: 2015-04-06
Posts: 46

Re: kind of the triangle

5.    A triangle ABC
The angles achieve the following relationship :Cos(B)+Cos(C)=Sin(A)
what kind of this triangle?

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#7 2015-04-10 05:23:49

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,138

Re: kind of the triangle

Are you giving us these as challenges or because you cannot do them and want help?

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#8 2015-04-10 05:33:54

hussam
Member
Registered: 2015-04-06
Posts: 46

Re: kind of the triangle

bob bundy wrote:

Are you giving us these as challenges or because you cannot do them and want help?

Bob

hi bob;

when i need help so i write in the (help me page)

i dont challenge any one

i give these exercises because MR Mathisfun sayed

MathsIsFun wrote:

Welcome to the Exercises section of the forum smile

Please contribute some exercises to help people who are still learning what you already know

Hussam

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#9 2015-04-10 05:47:42

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,138

Re: kind of the triangle

hi Hussam,

OK.  Thanks.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#10 2015-04-10 05:51:34

hussam
Member
Registered: 2015-04-06
Posts: 46

Re: kind of the triangle

so, shall i  provide more ?

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#11 2015-04-10 05:52:57

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,138

Re: kind of the triangle

Give me a chance to try these first.  smile

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#12 2015-04-10 05:55:56

hussam
Member
Registered: 2015-04-06
Posts: 46

Re: kind of the triangle

Q4 is correct!

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#13 2015-04-10 05:56:56

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,138

Re: kind of the triangle

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#14 2015-04-10 06:29:28

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,138

Re: kind of the triangle

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#15 2015-04-10 15:30:48

hussam
Member
Registered: 2015-04-06
Posts: 46

Re: kind of the triangle

hi bob;

Q3 is correct !

Q5; there is another situation: C=90

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#16 2015-04-10 15:36:48

hussam
Member
Registered: 2015-04-06
Posts: 46

Re: kind of the triangle

6.  A  triangle ABC
The angles achieve the following relationship :Sin(A)+Cos(A)=Sin(B)+Cos(B)
what kind of this triangle?

Last edited by hussam (2015-04-10 16:41:36)

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#17 2015-04-10 16:43:56

hussam
Member
Registered: 2015-04-06
Posts: 46

Re: kind of the triangle

7.  A  triangle ABC
The angles achieve the following relationship :[Sin(A)]^2=[Sin(B)]^2+[Sin(C)]^2
what kind of this triangle?

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#18 2015-04-10 17:41:53

hussam
Member
Registered: 2015-04-06
Posts: 46

Re: kind of the triangle

8.    A  triangle ABC
The angles achieve the following relationship :[Sin(A)]^2=Cos(C).Cos(A-B)
what kind of this triangle?

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#19 2015-04-10 19:01:07

hussam
Member
Registered: 2015-04-06
Posts: 46

Re: kind of the triangle

(the final of the kind of the triangle exercises).   
9. A  triangle ABC
The angles achieve the following relationship :[Sin(A)]^2+[Sin(B)]^2+[Sin(C)]^2=2
what kind of this triangle?

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#20 2016-04-22 02:34:20

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: kind of the triangle

Ans9. one of the angles is a right angle.


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#21 2016-04-22 02:47:31

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: kind of the triangle

ans.8 Angle  B is a right angle.


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#22 2016-04-22 02:48:50

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: kind of the triangle

Q.7 A is aright angle.


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#23 2016-04-22 02:54:57

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: kind of the triangle

Q6. either A=B or C is a right angle.


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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