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#1 2014-02-07 19:12:03

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,056

trigonometry#5

A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7 m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is 36° and that of the top of the flagstaff is 45° .Find the height of the tower.

P.S:-I constructed a diagram but I am not able to deal with 36° without using trigonometric table. Pls. help.

View Image: trigo.gif

friendship is tan 90°.

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#2 2014-02-07 20:33:13

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,547
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Re: trigonometry#5

I think using a table is okay in this case


'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'
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#3 2014-02-07 23:00:03

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 95,902

Re: trigonometry#5

Hi;


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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#4 2014-02-07 23:44:18

bob bundy
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Registered: 2010-06-20
Posts: 7,013

Re: trigonometry#5

hi Niharika,

I'm sure tables (or maybe a calculator) is acceptable here.  Trying to get a value for tan 36 without,  is going to be a tough one.  eek

Bob


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

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#5 2014-02-08 01:11:41

Nehushtan
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Registered: 2013-03-09
Posts: 618
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Re: trigonometry#5


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#6 2014-02-08 01:32:03

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,547
Website

Re: trigonometry#5

We can do the nested use of this formula


'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 2014-02-08 01:59:58

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: trigonometry#5

Hi niharika_kumar,

Perhaps the simplest method is to use De Moivre's formula, taking x= pi/5

Expand LHS and equate the imaginary parts

We can then easily solve it as a quadratic, putting y=sin(x)^2:

Hence,


and

and


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#8 2014-02-08 02:07:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 95,902

Re: trigonometry#5

Hi;

The polynomial for cos(x/5) has a neat factorization so it is very easy.


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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#9 2014-02-08 02:15:00

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: trigonometry#5

Hi,

Yes, that's also good.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#10 2014-02-11 16:58:55

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,056

Re: trigonometry#5

thanks
got it now.
will do some more study on De Moivre's formula.


friendship is tan 90°.

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#11 2014-02-11 17:25:02

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: trigonometry#5

You're welcome.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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