Math Is Fun Forum

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?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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 .

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)

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?

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?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

hussam

Member

Registered: 2015-04-06

Posts: 46

Re: kind of the triangle

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

Welcome to the Exercises section of the forum

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

Hussam

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

hussam

Member

Registered: 2015-04-06

Posts: 46

Re: kind of the triangle

so, shall i  provide more ?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

hussam

Member

Registered: 2015-04-06

Posts: 46

Re: kind of the triangle

Q4 is correct!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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

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)

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?

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?

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?

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.}

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.}

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.}

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.}