Math Is Fun Forum

thedarktiger

Member

Registered: 2014-01-10

Posts: 91

Point inside a square

Let P be a point inside square ABCD such that PA = 1, PB = 2, and PC = 3. Find \angle APB.

So how to do this one? I can't find any angles aaagggh

Thanks!

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Good. You can read.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Point inside a square

Hi;

I am getting 135°

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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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Point inside a square

hi thedarktiger,

This one is similar to a problem we were asked about some time back:

http://www.mathisfunforum.com/viewtopic … 27#p159127

It was quite a challenge as you can see .  The method that was 'voted' best can be applied here:

Rotate the diagram by 90 degrees around point A.  Call the rotated point P'

As AP has rotated 90 => P'AP is 90.  Also AP' = AP so this triangle is isosceles => angle APP' = 45 and P'P =   √2

In triangle BPP' all three sides are known so the cosine rule can be used to calculate angle P'PB.

Add 45 and hence get APB.

Bob

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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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

thedarktiger

Member

Registered: 2014-01-10

Posts: 91

Re: Point inside a square

Thanks guys! Makes sense to rotate.
It looks like it is 135.
ಠ_ಠ  ಥ_ಥ  ಠ▃ಠ  ლ(ಠ_ಠლ)

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Good. You can read.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Point inside a square

hi

I realised today I had the wrong diagram.  Revised attempt here.

Same idea but rotate around B and work out P'P from isosceles right angled triangle BPP'

Then cosine rule on APP'

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

thedarktiger

Member

Registered: 2014-01-10

Posts: 91

Re: Point inside a square

ᶘᵒᴥᵒᶅ
Still works!

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Good. You can read.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Point inside a square

But now I get the same answer as bobbym. 

Always a relief when that happens.

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Point inside a square

Hi;

To use latex here you must use the math tags and not $.

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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.

RandomPieKevin

Member

Registered: 2015-07-02

Posts: 29

Re: Point inside a square

^^ Why does it just say Submit with a img symbol? ^^

Last edited by RandomPieKevin (2015-07-27 02:43:15)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Point inside a square

hi RandomPieKevin

There was a } missing in the above post which I have added for you.  Unless the bit 'under the square root' is a single symbol you have to enclose all in curly brackets, plus the one to close off the fraction numerator.

What is the 'it' referred to above.  I assume you were trying to add an image.

Bob

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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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob