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Pythagorean assumptions

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Joined: 09 May 2004
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Pythagorean assumptions [#permalink]  28 Jun 2004, 09:23
Hey guys,

I have a few triangle issues that keep coming up on my studying. Any help would be greatly appreciated.

1) If I am given a right triangle and given that the hypoteneuse is 5, can I assume that the other sides are 3 and 4 by assuming that it is a Pythagorean triple?. I know that if it is the reverse, and I am given 3 and 4 as sides and I know it is a right triangle, I can assume the hypoteneuse is 5... but I make the assumption given the reverse order of information?

2) If I am given the sides 3 and 4 of a triangle that LOOKS LIKE it has a right triangle, and I need to find the hypotenuese side, can I assume that the hypoteneuse is 5 even if it doesn't say explicitly anything about it having a right angle?

3) Also, are there any Pythagorean triples (2/4/5 - 6/8/10, etc) where I can assume it is a 30-60-90 triangle?

On DS especially, I seem to make a lot of assumptions that prove incorrect (e.g. that I can find a side of a triangle with the info given, when I really cannot), and I just want to make sure I have my rules correct.

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Re: Pythagorean assumptions [#permalink]  28 Jun 2004, 09:30
cs77 wrote:
Hey guys,

I have a few triangle issues that keep coming up on my studying. Any help would be greatly appreciated.

1) If I am given a right triangle and given that the hypoteneuse is 5, can I assume that the other sides are 3 and 4 by assuming that it is a Pythagorean triple?. I know that if it is the reverse, and I am given 3 and 4 as sides and I know it is a right triangle, I can assume the hypoteneuse is 5... but I make the assumption given the reverse order of information?

Of course, no, because there are a lot of other triangles with sides such as (5/sqrt(2), 5/sqrt(2), 5) which have right angle.

cs77 wrote:

2) If I am given the sides 3 and 4 of a triangle that LOOKS LIKE it has a right triangle, and I need to find the hypotenuese side, can I assume that the hypoteneuse is 5 even if it doesn't say explicitly anything about it having a right angle?

No, unless it is said that the triangle IS right.

cs77 wrote:

3) Also, are there any Pythagorean triples (2/4/5 - 6/8/10, etc) where I can assume it is a 30-60-90 triangle?

No, because triangle with angles 30-60-90 has one side of irrational length(which is not rational, not a fraction of m/n, where m,n - are integers).

cs77 wrote:

On DS especially, I seem to make a lot of assumptions that prove incorrect (e.g. that I can find a side of a triangle with the info given, when I really cannot), and I just want to make sure I have my rules correct.

OK. I think I clarified it well enough.
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Thanks very much Emmanuel for clarifying. I have missed a handful of questions because I was confused on what I could assume and what I couldn't. Thks!
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