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

niharika_kumar
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From: Numeraland
Registered: 2013-02-12
Posts: 1,028

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

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

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 17,995
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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: 88,761

Re: trigonometry#5

Hi;


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

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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

bob bundy
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Registered: 2010-06-20
Posts: 6,468

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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From: London
Registered: 2013-03-09
Posts: 615
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Re: trigonometry#5


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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,995
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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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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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: 88,761

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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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: 1,028

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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