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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,051

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.

friendship is tan 90°.

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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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,917

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,916

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.

Bob

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

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,917

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

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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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,051

thanks

got it now.

will do some more study on De Moivre's formula.

friendship is tan 90°.

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

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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