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finding the third side of a Triangle with only length of two sides given.

hi guys,

I seem to have hit a roadblock. I have the length of two sides of a triangle, i want to find the length of the third side. Now let give some additional details.

IT is not a right angle triangle.

I do not have any additional information (like the area,perimeter,angles,etc). (Speechless)

I just have the length of the other two sides, in an excel sheet, is there any formula to find the third side?

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Re: finding the third side of a Triangle with only length of two sides given.

There are an infinite number of possibilities for this third length of the triangle. The length can be anywhere in the region $\displaystyle \displaystyle \begin{align*} 0 \textrm{ cm} < l < 21 \textrm{ cm} \end{align*}$.

Re: finding the third side of a Triangle with only length of two sides given.

So your telling me there is no other way to find out the length of the other side? :(

Re: finding the third side of a Triangle with only length of two sides given.

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Originally Posted by

**satya1987** So your telling me there is no other way to find out the length of the other side? :(

Not without some more information, like the angle between the two known sides (then you could use the Cosine Rule) or the perimeter or area or something...

Re: finding the third side of a Triangle with only length of two sides given.

Quote:

Originally Posted by

**satya1987** So your telling me there is no other way to find out the length of the other side?

No, he is not saying that.

There are infinitely many solutions, **there is **__no unique__ solution.

If you know the measure of that *included angle*, then it is easy.

Re: finding the third side of a Triangle with only length of two sides given.

Hello, satya1987!

Where did this question come from?

And *who* would ask such a silly question?

Quote:

I have the length of two sides of a triangle.

I want to find the length of the third side.

It is not a right angle triangle.

I do not have any additional information (like the area,perimeter,angles,etc).

I just have the length of the other two sides.

Is there any formula to find the third side?

Attachment 26860

No, there isn't.

The third side could be *any* value from 0 to 21.

Re: finding the third side of a Triangle with only length of two sides given.

thanks guys, No one asked me this question. I am doing some data collecting using GIS software. I have these two sides and was wondering whether there was someway to calculate the third side. If it was a right angle triangle i could have used pythagoras., but alas. thanks guys for your help!!

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Re: finding the third side of a Triangle with only length of two sides given.

One way of thinking about this is to start with your original picture.Attachment 26865

Now imagine the angle opening and closing. It can close to to angle 0 in which case the "third side" has length 0. It can open to angle 180 degrees in which case the "third side" has length 8+ 13= 21 cm. Of course, those two extreme cases don't really give triangles. That is why the answer is 0< l< 21.

Re: finding the third side of a Triangle with only length of two sides given.

yes i do know that we need either the angle,perimeter or area to get the length, however i was thinking there might be another way you know. Like drawing a circle or something and find the length. thanks a lot guys!

Re: finding the third side of a Triangle with only length of two sides given.

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Originally Posted by

**Prove It** There are an infinite number of possibilities for this third length of the triangle. The length can be anywhere in the region $\displaystyle \displaystyle \begin{align*} 0 \textrm{ cm} < l < 21 \textrm{ cm} \end{align*}$.

I don't want to pick at you but ....

Refering to the attached image the shortest possible length of the 3rd side is 5 (The included angle between the two known sides is 0°) and of course the longest possible side is 21.

Re: finding the third side of a Triangle with only length of two sides given.

Quote:

Originally Posted by

**earboth** I don't want to pick at you but ....

Refering to the attached image the shortest possible length of the 3rd side is 5 (The included angle between the two known sides is 0°) and of course the longest possible side is 21.

Yes that's true, I forgot that the two other lengths weren't the same. I was thinking more visually, in terms of opening and closing the lengths...