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

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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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,421

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

Sometimes I deliberately make mistakes, just to test you!

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

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

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

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

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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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,421

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

Sometimes I deliberately make mistakes, just to test you!

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

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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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,421

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

Sometimes I deliberately make mistakes, just to test you!

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

so, shall i provide more ?

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,421

Give me a chance to try these first.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you!

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

Q4 is correct!

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,421

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you!

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,421

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you!

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

hi bob;

Q3 is correct !

Q5; there is another situation: C=90

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

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

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

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

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

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

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

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

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

(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha

{Gods rejoice at those places where ladies are respected.}

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