Homework Help: geometry inequality triangles help if you can

Posted by Knights on Monday, December 31, 2012 at 11:58am.

Two sides of an obtuse triangle are 16 and 21. How many possible lengths are there for the third side, if it is a positive integer?

i know that in an obtuse triangle

a^2+b^2<c^2
a+b>c
but i tried plugging in and it wont work so couldyou guys help me?

btw merry christmas and happy new year

geometry inequality triangles help if you can - Reiny, Monday, December 31, 2012 at 1:35pm
First let's establish the domain for the third side

let the third side be c
c+16>21 ----> c > 5
c+21 > 16 ----> c > -5 , obviously
21 + 16 > c ---> c < 37

so to be a triangle in the third side must be
5 < c < 37

Now to be obtuse
c^2> 21^2+16^2
c^2 > 697
c > 26

could one of the other angles be obtuse ?
21^2 >c^2 + 16^2
c^2 < 185
c < 14

16^ > c^2 + 21^2
c^2 < a negative, which is not possible

So for the angle opposite the third side to be obtuse,
26 < c < 37

For the angle opposite the side 21 to be obtuse,
5 < c < 14
geometry inequality triangles help if you can - Knights, Monday, December 31, 2012 at 1:39pm
thanks a lot the answer is 18 right?

merry christmas and happy new year to y
geometry inequality triangles help if you can - Reiny, Monday, December 31, 2012 at 2:08pm
No, 18 does not work.

Notice my two possible solutions, .....

So for the angle opposite the third side to be obtuse,
26 < c < 37
So the third side could be 27, 28, 29, 30 31 32 33 34 35 or 36

For the angle opposite the side 21 to be obtuse,
5 < c < 14
so the third side could be 6 7 8 9 10 11 12 or 13

make a sketch using one of the answers and illustrate that the angle must be obtuse by using the cosine law.

Also test it with your 18 to show it does not work
geometry inequality triangles help if you can - Knights, Monday, December 31, 2012 at 9:30pm
I meant the total number of possibilities. Thanks anyway!

Answer this Question

Related Questions

Geometry REPOST - Please try to help me out as much as possible -- this homework...
Algebra - Need help with these-- 21. Find the possible values of a, of the ...
geometry - Two triangles each have adjacent sides of length 120 feet and 180 ...
Math Question - Which one of the following pairs of triangle must be similar? a...
math - if possible,draw two isosceles triangle in which all the equal-length ...
Geometry - 1. The sides of a triangle have lenghts x, x+4, and 20. Specify those...
Geometry - Two triangles are similar. The lengths of the sides of the smaller ...
geometry - A triangle has sides x,x+7 , x+ 8. The value of x must fall between ...
Math - If all of the following triangles have the same perimeter, which has the ...
Geometry - An Isosceles triangle has a 96degree angle. What are the measures of ...

For Further Reading

First Name:
School Subject:
Answer: