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Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

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Which Values make the triangle obtuse?

The sides of a triangle have lengths 9,13 and k, where 'k' is a integer. For how many values of "k" is the triangle obtuse?

Also tell me how u did the calculation

Last edited by Agnishom (2011-01-29 22:51:12)

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bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Which Values make the triangle obtuse?

Hi Agnishom;

I am getting k >=16.

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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.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Which Values make the triangle obtuse?

How u did the calculation?

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'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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Which Values make the triangle obtuse?

An obtuse triangle must satisfy this condition.

So

k = 15.81.

So one answer is when k>=16 < 22 and k is an integer. At 22 the triangle degenerates into a straight line. So it is not obtuse.

Of course we could also choose:

k = 9.38

So k = 9,8,7,6,5 also yield an obtuse triangle. Do you see why k must be bigger than 4?

So I am getting 11 integer values all together.

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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.

sameer mishra

Member

Registered: 2010-08-27

Posts: 64

Re: Which Values make the triangle obtuse?

frist let k is biggest side of triangle
then for formation of triangle {sum of two smallest side will always greater than biggest side}
(13+9)>k
k<22.................(1)

let in above triangle ABC  the k is side infront of angle A

then for obtuse angle cosA<0
hence cosA=(9^2 +13^2-K^2)/2*9*13
2nd lowest statement emplies...........9^2 +13^2<k^2

on solving above inequality the accepted valu of k is greater than 15.81
hence integer values are 16 17 18 19 20 21 (total 6 integer value)

"NOW CHANGING CONDITION"

i.e 13 is biggest side
13^2>k^2+9^2
    -9.38< k<9.38
but k+9>13
k>4
hence total integer valu 5 6 7 8 9
hence total no of integer value will be 11