# Numbers representing sides of a triangle

• Jan 5th 2010, 03:27 PM
Jubbly
Numbers representing sides of a triangle
Hello. I was wondering how do you find out how numbers can represent the lengths of the sides of a triangle that has a square root and just numbers.

An example would be this one: 7, √5, 3√6. would this be an obtuse triangle?

Also would anyone care to explain? Thanks.(Happy)

Is it a right, acute, or obtuse?
• Jan 5th 2010, 03:32 PM
vonflex1
any three numbers can represent the sides of a triangle
if you don't include conditions on the angles.
• Jan 6th 2010, 01:46 PM
buggerzapper
using SSS we can figure out the name of any triangle, and with a bit of math, the exact angles

say the numbers were 3 4 and 5 know that that triagle is a right triangle, and with a little math one could find it is 90 36.87 and 53.13
• Jan 6th 2010, 01:50 PM
e^(i*pi)
Quote:

Originally Posted by Jubbly
Hello. I was wondering how do you find out how numbers can represent the lengths of the sides of a triangle that has a square root and just numbers.

An example would be this one: 7, √5, 3√6. would this be an obtuse triangle?

Also would anyone care to explain? Thanks.(Happy)

Is it a right, acute, or obtuse?

You can, but the explanation requires trig to find out.

The cosine rule says that $\displaystyle c^2=a^2+b^2-2abcosC$ and so

$\displaystyle cosC = \frac{a^2+b^2-c^2}{2ab}$

Where $\displaystyle a, b, c$ are sides and $\displaystyle A, B, C$ are angles opposite sides $\displaystyle a,b,c$ respectively

Law of cosines - Wikipedia, the free encyclopedia