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

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,852
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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'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bob bundy
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Registered: 2010-06-20
Posts: 6,298

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


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: The Complex Plane
Registered: 2011-01-29
Posts: 15,852
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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'
'Humanity is still kept intact. It remains within.' -Alokananda

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

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,852
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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'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bob bundy
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Registered: 2010-06-20
Posts: 6,298

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


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: The Complex Plane
Registered: 2011-01-29
Posts: 15,852
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'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,298

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


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

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