Triangle

**Makron** · January 31st 2011, 11:34 AM

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

**TheEmptySet** · January 31st 2011, 11:40 AM

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

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

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

Can you finish from here?

**Makron** · January 31st 2011, 11:56 AM

Thank you for helping =)

but the angle is unknown ?

**masters** · January 31st 2011, 11:58 AM

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 $x$ , then $5 < x < 19$

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

**Makron** · January 31st 2011, 12:00 PM

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

**HallsofIvy** · January 31st 2011, 04:32 PM

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

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