1. ## Triangle

Hello

A triangle has one side that is 7 and another side that is 12. What it the max and min value for the third side.

Thank you for any help

2. Originally Posted by Makron
Hello

A triangle has one side that is 7 and another side that is 12. What it the max and min value for the third side.

Thank you for any help
If you know the law of cosines then

$\displaystyle c^2=a^2+b^2-2ab\cos(\theta)$

$\displaystyle c^2=49+144-168\cos(\theta)$

Can you finish from here?

3. Thank you for helping =)

but the angle is unknown ?

4. Originally Posted by Makron
Hello

A triangle has one side that is 7 and another side that is 12. What it the max and min value for the third side.

Thank you for any help
Hi Makron,

If the third side is $\displaystyle x$, then $\displaystyle 5 < x < 19$

Essentially, the third side must be greater then the difference of the other two sides, but less than their sum.

5. thank you but I would like to know how to complete the ekvation that "Emptyset" posted

6. The equation was $\displaystyle c^2= 49+ 25- 168cos(\theta)$. The angle $\displaystyle \theta$ can be any angle between 0 and 180 degrees. What is that equation if $\displaystyle \theta= 0$? What if $\displaystyle \theta= 180$?