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#1 2013-03-22 17:48:35

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,752
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Trigonometric Equation

If in a triangle,

Then,
What is the value of sin angle A?

Is it 8/27?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#2 2013-03-22 20:20:56

bob bundy
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Registered: 2010-06-20
Posts: 7,059

Re: Trigonometric Equation

hi Agnishom

How did you get that?  It's not what I'm getting.

Here's my method.

SINE RULE is:

So I put

and re-arranged to get

Different values of k will make different sized circles but all the resulting triangles will be similar => same three angles.

So it is ok to take a = √6,   b = 2√2,     c = 3√3

Use the cosine rule to get cosA and hence sinA.

I made it

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 2013-03-22 20:38:29

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,752
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Re: Trigonometric Equation

bob bundy wrote:

hi Agnishom

SINE RULE is:

So I put

and re-arranged to get

I have the following doubts:

I. How did you do the rearrangement?
II. How do you know what to put for a?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#4 2013-03-22 20:56:16

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,752
Website

Re: Trigonometric Equation

Okay thanks I managed to understand this

lawofsines.png


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#5 2013-03-22 23:07:06

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,059

Re: Trigonometric Equation

hi Agnishom,

Glad you understand it.  Your method and mine are essentially the same; I used k; you have t; and then I let k=1.  In yours the t cancels out. 

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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#6 2013-03-23 02:29:38

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,752
Website

Re: Trigonometric Equation

smile Yeah Thanks! I had difficulty understanding the cancellation


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#7 2013-03-23 06:09:28

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,059

Re: Trigonometric Equation

Two triangles with sides in the same ratio are similar.  So the angles are the same.  Therefore you can just call t = 1 without losing any of the problem's conditions.

That's why it cancels out of the cosine rule step.

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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