Can You Find Non-Congruent Triangles…Any takers?

[The Highlander]

count the number of different (in the sense of non-congruent) triangles that satisfy the conditions.

Hmmm, can anyone describe, sketch or draw triangles that satisfy the conditions of my ("Part 8)") example that are non-congruent? (Or, indeed, ones that satisfy any of the other parts in the original question.)
I'm struggling to find them but don't discount the possibility that there may well be such constructions and I just can't see them.
Any takers?

 

[Dr.Peterson]

Hmmm, can anyone describe, sketch or draw triangles that satisfy the conditions of my ("Part 8)") example that are non-congruent? (Or, indeed, ones that satisfy any of the other parts in the original question.)
I'm struggling to find them but don't discount the possibility that there may well be such constructions and I just can't see them.
Any takers?

Why should the problem you made up determine what the actual problem is about?

In any case, I would not be surprised if the answer to most of the questions is 1; that wouldn't bother me a bit.

I'm just waiting to learn more about the problem. But I suspect that won't happen.

 

[lookagain]

Why should the problem you made up determine what the actual problem is about?

When trigonometry problems are presented in the forums, sometimes helpers' advice goes off on tangents.

 

[The Highlander]

When trigonometry problems are presented in the forums, sometimes helpers' advice goes off on tangents.

That is doubtless true but, if you are referring to my attempt to help the OP, then I have to say that I stand by my interpretation of the OP’s “situation” and reason for their post.

I still think (though I could be wrong, ofc) that this problem relates more to basic Geometry (construction of plane figures) rather than Trigonometry (except in the strictest sense: that Trigonometry could be regarded as anything to do with the ‘measurement(s) of three sided figures’).

Furthermore, given that the OP posted simply a reproduction of their problem with no further comment/explanation or identification of what their ‘difficulty’ was, I think the odds are still in favour of this being a post from an ‘early learner’ (in the 10 or 11 to 13 or 14 years of age bracket?) in Maths rather than someone in more advanced study who might have been tasked with considering “theorems like SAS and SSA”; if the latter were the case then I think the OP would have included a more explicit reference to what they were having problems with.

Why should the problem you made up determine what the actual problem is about?

And you accuse me of “hostility”??? (Here, for example: Post #14!)

There is absolutely no reason why the example I ‘made up’ should “determine what the actual problem is about” and I did not suggest that it ought to!

I made it absolutely clear that I was asking for an example from any of the parts in the original question where non-congruent triangles that satisfied the given parameters existed; you appear to be letting your personal dislike of me get the better of your usually phlegmatic criticisms of my posts

In any case, I would not be surprised if the answer to most of the questions is 1; that wouldn't bother me a bit.

Well, unless you (or any other) can come up with some examples of these non-congruent triangles that satisfy the given conditions (in any part of the original question or my “made up example”) then I would suspect that the answer to most of the questions might rather be 2 but, right or wrong, that wouldn’t bother me either! (Though, I have to say, this comment almost looks like an attempt to distance yourself from your initial post without actually admitting it may have been a bit wide of the mark?)

I'm just waiting to learn more about the problem. But I suspect that won't happen.

I think you are probably absolutely right on that point; it seems unlikely now that the OP is about to make any further ‘contributions’.

Maybe now that gives you (or @Steven G) an ideal opportunity to post your own ‘solutions’ to the question as it was posted?

I’m sure that would be of interest to any future readers of the thread and, as always, I’d be happy to defer the greater expertise of the “Elites” (and admit I was wrong) if any care to post such a solution.

 

[lookagain]

That is doubtless true but, if you are referring to my attempt to help the OP, then ...

Let us enjoy my play on words for what it is: trigonometry, tangents.

By the way, every time I read your posts, I have to turn my binoculars around the
other way to compensate because of your larger text.

 

[The Highlander]

Let us enjoy my play on words for what it is: trigonometry, tangents.

I did wonder if you were attempting some kind of (excruciating) pun there. ?
But trigonometry & tangents? They're not really in the same branches of Maths, are they? (Triangles vs. Circles?)
I mean the connection is very tenuous; maybe not enough to make a sound gag out of?
At least you enjoyed it, however. ?

By the way, every time I read your posts, I have to turn my binoculars around the
other way to compensate because of your larger text.

Well, there's your chance to get back in with the rest of the "Elites"! (I believe you may have upset some of them yourself in the past?)
My use of "larger text" was one of the very first things that caused a number of them to turn against me but there are some things that I just like BIG! ?
(So no likelihood of any change there, I'm afraid. ?)

 

[lookagain]

But trigonometry & tangents? They're not really in the same branches of Maths, are they?

I am going to spell it out for you:

\(\displaystyle tangent \ = \ \dfrac{sine}{cosine}\)

 

[The Highlander]

I am going to spell it out for you:

\(\displaystyle tangent \ = \ \dfrac{sine}{cosine}\)

Ah, I see,, you were referring to the Tangent RATIO.
When you wrote: "goes off on tangents" my mind immediately locked onto the idea of a straight line touching (from the Latin tangere: to touch) a circle (or other curve) at a single point and heading away from said curve in its 'direction' at that point, hence the idea of "going off at a tangent" but I see the connection you were aiming for now and it certainly increases the humorous element once you get the joke.
Thank you for explaining it and excuse my one track mind.

 

[mmm4444bot]

a straight line … heading away from [a tangent point] in its 'direction'

Could that be 'directions'?

?
[imath]\;[/imath]

 

[The Highlander]

Could that be 'directions'?

?
[imath]\;[/imath]

Yes, of course it could be "directions" or it could just be a direction that has a positive or negative sense but do you really have nothing better to do with your time than to nitpick at everything I say?
(Maybe you could go find some other posts to edit so that say what you want instead of what the author intends?)