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

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
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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'
I'm not crazy, my mother had me tested.

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

Bob
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Registered: 2010-06-20
Posts: 10,053

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

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#3 2013-03-22 20:38:29

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
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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'
I'm not crazy, my mother had me tested.

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

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
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'
I'm not crazy, my mother had me tested.

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

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

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

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
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'
I'm not crazy, my mother had me tested.

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

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

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

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