Talk:Right triangle

Opening nomenclature and definitions
I note that this page is a translation (modified, I believe) of the French Wikipédia article "Triangle rectangulaire". I am a professional translator and have met some of the issues that arise in translating this topic. If no one disagrees, and if I remember, I propose amending the opening few words and the second paragraph as follows:

"A right triangle (or right-angled triangle as it is known in the UK) ..."

and

"The side opposite the right angle is called the hypotenuse (side [BC] in the figure below). There is no special name for the other two sides, so they are simply called "the other two sides". (Some languages give them special names: in French the other two sides are called the "cathètes", while the Italians call them "cateti" . For some reason these learned names have never caught on in English, though "legs" and "catheti" (singular "cathetus") have been attempted.) Side [AB] is said to be adjacent to angle α and opposite angle β, while side [AC] is adjacent to angle β and opposite angle α. With respect to angle α, side [AB] is said to be the adjacent side and [AC] the opposite side. --UBJ 43X (talk) 11:37, 5 May 2009 (UTC)


 * I incorporated your first suggestion in the article. I disagree with the second. I added a Terminology section. The terms in that section are all fairly common in English usage. Finell (Talk) 03:58, 15 May 2009 (UTC)

Your incorporation of US/UK terms is neater than mine, thanks. Re my proposed paragraph on the names of the sides of the right-angled triangle (above): my searches on the web suggest that "leg" is common in the USA (it occurs on math websites for children) but rare or unknown in the UK. It may be worth adding this apparent difference of usage in my proposed paragraph of terminology. I am UK born and bred and I don't recall ever hearing the terms "cathetus" or "leg" when I was learning geometry at school in the 1970s. We invariably called the short sides "the other two sides" (when stating Pythagoras's theorem) or "the opposite/adjacent side" (to whichever angle or side was under discussion, when discussing trigonometry). The Penguin Dictionary of Mathematics, a British work, contains an entry for "leg" but none for "cathetus", and it does not use either term when defining the right-angled triangle or when stating Pythagoras's theorem (in the latter case it refers to them as "the sides containing the right angle"). UBJ 43X (talk) 09:17, 19 January 2011 (UTC)

"Other properties"
I removed this section:


 * For any integer n greater than or equal to 3, one can always find a triangle with a length of one side of the right angle and n is the length of the other two sides are whole numbers. Indeed:


 * If $$n$$ is an even number, $$n = 2k$$. Take the length of the other side of the right angle equal to $$k^2-1$$. The Pythagorean theorem then gives a hypotenuse of length $$k^2+1$$.
 * If $$n$$ is an odd number, $$n = 2k + 1$$. Take the length of the other side of the right angle equal to $$2(k^2+k)$$. The Pythagorean theorem then gives a hypotenuse of greater than or equal to $$2(k^2 + k) + 1$$.

These confuse the side with its square. —Tamfang (talk) 04:46, 13 November 2009 (UTC)

practical recommendations
Recommend adding a section for practical use and to help my homework:

1. List the angles and length of each side of a 3-4-5 triangle.

2. List the angles and length of each side of a 1-1-square root of 2 triangle

3. List the angles and length of each side of a 1, 2 square root of 3 triangle (which I know the answer, it's a 30-60-90 triangle).

Also include pictures of these.

The title of the section could be "practical information" JB50000 (talk) 05:53, 3 January 2010 (UTC)


 * Wikipedia is not a crystal ball, and yet I make this prediction: Not gonna happen. —Tamfang (talk) 08:06, 3 January 2010 (UTC)


 * Do your own homework. -Milesman34 —Preceding undated comment added 13:45, 10 November 2016 (UTC)

Etymology
A word ὀρθόςγωνία does not exist. The source is inaccessible to me but it looks made up. I would give the expression ὀρθὴ γωνία a chance. See also Ορθογώνιο τρίγωνο (be warned that it is in a different language though). --Yecril71pl (talk) 11:52, 18 June 2021 (UTC)

Practical Applications
I added the formula of the length of the hypotenus in the first section of the article for a reason that is vitally important to everyone who uses math in practical applications so I want other editors to consider this point very seriously before removing my edit. My reason for adding that formula applies generally, so let's develop a policy for adding practical information to wikipedia articles using this as an example. Many many peple will go to this article in search of the formula for calculating the length of the hypotenus in terms of the other two sides and we want such formulas easily accessible in addition to the need for rigorous formal presentations. Can we find a way to integrate the material to serve BOTH the academic and practical needs? Thank you VERY MUCH. Rtdrury (talk) 13:49, 9 May 2023 (UTC)


 * This formula is already mentioned 2–3 other times later on in the article, and is the subject of the article Pythagorean theorem. I don't think this version is especially helpful to add to the lead section. I re-ordered the sub-sections of the 'properties' section to put this equation at the top though. –jacobolus (t) 17:24, 9 May 2023 (UTC)