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## #1 2016-03-22 13:36:48

Monox D. I-Fly
Member
Registered: 2015-12-02
Posts: 857

### [ASK] Tan 36°

I was reading about the area of regular pentagon and it said that

. Where did it come from? Does
always equal
? If yes, what is the proof?

Last edited by Monox D. I-Fly (2016-03-22 13:38:07)

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## #2 2016-03-22 13:45:42

evene
Member
Registered: 2015-10-18
Posts: 272

### Re: [ASK] Tan 36°

is only true in Radians. I figured that out with a calculator.

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## #3 2016-03-22 14:08:14

Monox D. I-Fly
Member
Registered: 2015-12-02
Posts: 857

### Re: [ASK] Tan 36°

Ummm... Can you prove it algebraically?

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## #4 2016-03-22 16:44:39

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

### Re: [ASK] Tan 36°

That is not always true.

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.

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## #5 2016-03-23 08:37:08

bob bundy
Registered: 2010-06-20
Posts: 8,137

### Re: [ASK] Tan 36°

hi Monox D. I-Fly

Start with an isosceles triangle ABC with angle C = 36, and A = B = 72.

Bisect A and continue this line to cut BC at D.  E is the 'foot' of the perpendicular from D to AC.

There are two more isosceles triangles in this diagram; ADC is 36,36, 108; and ABD is 36,72,72 again.  I have marked the angles of 36 with a dot to avoid too much labelling on the diagram.

Let AC = BC = x and AB = AD = 1.

As ABC and ABD are similar, the ratios of corresponding sides are equal:

This quadratic has two solutions but as we know x is positive we can discard the negative solution:

So

As x has a square root in its form and the above also I will simplify by working with tan squared.

Now errors can occur if you square and then square root an expression.  But in this case we can safely take the positive root as we know tan(36) will be positive.

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

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## #6 2016-03-23 15:46:37

Monox D. I-Fly
Member
Registered: 2015-12-02
Posts: 857

### Re: [ASK] Tan 36°

Thank you very much, bob. Also, I am surprised that bobbym and bob bundy aren't the same person.

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## #7 2016-03-23 16:13:49

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

### Re: [ASK] Tan 36°

I often thought that myself. Other times, I was sure it was false. But you have raised a cloud of uncertainty around the whole question. I will have to investigate further... By the way, I hope Bob does not bar you.

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.

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## #8 2016-03-23 16:18:23

Monox D. I-Fly
Member
Registered: 2015-12-02
Posts: 857

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## #9 2016-03-23 18:30:30

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

### Re: [ASK] Tan 36°

Checking thoroughly, I am in Florida while Bob resides in the UK. I calculate a 99.3% chance that we are two separate entities.

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.

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## #10 2016-03-25 00:38:57

Monox D. I-Fly
Member
Registered: 2015-12-02
Posts: 857

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## #11 2016-03-25 04:03:55

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

### Re: [ASK] Tan 36°

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.

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