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TRIANGLE : 5.3 Solution of triangles
About solution of triangles, 5.3 the next sentence could be more accurate if the last section is added:
"Solution of triangles" is the main trigonometric problem: to find missing characteristics of a triangle (three angles, the lengths of the three sides etc.) when at least three of these characteristics are given , including at least one non-angular value.
Could somebody make this appropriate correction ?
- While appropriate for planar triangles, it is not appropriate for spherical triangles since AAA is a congruency condition there.--Bill Cherowitzo (talk) 03:17, 8 April 2018 (UTC)
In the introduction, it is written: "This article is about triangles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted."
For solution of non-Euclidian triangle, you will need more than AAA; you need R ( a non angular value ) to find the length of the sides... In the end exemple of non-planar geometry, the position of the corners give the ratio of surface, but still not the length of the sides... Duckkcud 2018-04-10 — Preceding unsigned comment added by Duckkcud (talk • contribs) 17:05, 10 April 2018 (UTC)
- The section specifically includes triangles on a sphere, so any statement made should also be applicable to that case. Also, in the spherical case, the lengths of the sides of the triangle are not measured in linear units (to do so you would need to know R the radius of the sphere, as you correctly point out) but rather in angular units referring to the central angles determined by the sides and this does not require knowledge of R. This, probably, is due to the astronomical applications, where R can not be accurately determined. See the main article Solving Triangles for more information on this. The example in the non-planar triangle section of this article is not germane to this question.
As this article on "Triangles" deals primarely on plane one, it should be normal to precise its properties without confusion. That is exactly precised in the article on "solution of triangle" in wiki: '...at least one of the side lengths must be specified...'
The surface, the perimeter can too serve to solution. But only angles, are not enough.
In the paragraph that I propose to correct, there is no reference to spherical triangle. So, it is an error to not mention what I propose. DUckkcud 2018 04 11 — Preceding unsigned comment added by Duckkcud (talk • contribs) 13:51, 11 April 2018 (UTC)
- The section, in its entirety is:
"Solution of triangles" is the main trigonometric problem: to find missing characteristics of a triangle (three angles, the lengths of the three sides etc.) when at least three of these characteristics are given. The triangle can be located on a plane or on a sphere. This problem often occurs in various trigonometric applications, such as geodesy, astronomy, construction, navigation etc.
What part of "The triangle can be located on a plane or on a sphere." do you not understand? Your statement is valid for planar triangles, and I have said so above, so I am not sure what you intend by bringing up sources which only refer to planar triangles.--Bill Cherowitzo (talk) 18:25, 11 April 2018 (UTC)
I should have written "in the sentence", not "in the paragraph". And calling an error was not appropriate. Excuse me. My intent is to take the occasion to say exactly how many and what inputs are necessary to solution a planar triangle
without confusion with spherical one.
"At least three" is a bit vague while the number 3 is the beauty of triangle. I still suggest: "when three of these characteristics are given , including at least one non-angular value on a plane." --Duckkcud 2018 04 11 — Preceding unsigned comment added by 22.214.171.124 (talk) 21:24, 11 April 2018 (UTC)
Semi-protected edit request on 22 August 2019
|This edit request has been answered. Set the |
- Not done: triangulation is already mentioned as a more general case so specific file format does not seem necessary. Melmann 10:03, 22 August 2019 (UTC)
Adding the area of a cevian triangle
Read the "Be Bold" statement so will add a short entry under "Figures inscribed in a triangle" for cevian triangles then pursue a separate entry for this subject.