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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
Registered: 2010-06-20
Posts: 8,137

### 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
Registered: 2010-06-20
Posts: 8,137

### 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

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
Registered: 2010-06-20
Posts: 8,137

### 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
Registered: 2010-06-20
Posts: 8,137

### Re: kind of the triangle

Give me a chance to try these first.

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

Q4 is correct!

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

bob bundy
Registered: 2010-06-20
Posts: 8,137

### 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
Registered: 2010-06-20
Posts: 8,137

### 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

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

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

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

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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