Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

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

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,062

### 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.

friendship is tan 90°.

Offline

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,850
Website

### 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'
I'm not crazy, my mother had me tested.

Offline

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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### 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.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

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

bob bundy
Registered: 2010-06-20
Posts: 8,322

### 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.

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

Offline

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

Nehushtan
Member
Registered: 2013-03-09
Posts: 913
Website

Offline

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,850
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'
I'm not crazy, my mother had me tested.

Offline

## #7 2014-02-08 01:59:58

gAr
Member
Registered: 2011-01-09
Posts: 3,481

### 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."

Offline

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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### 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.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

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

gAr
Member
Registered: 2011-01-09
Posts: 3,481

### 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."

Offline

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

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,062

### Re: trigonometry#5

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

friendship is tan 90°.

Offline

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

gAr
Member
Registered: 2011-01-09
Posts: 3,481

### 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."

Offline