计算三角形的第三个点的坐标 [英] Calculating the coordinates of the third point of a triangle

问题描述

好吧，我知道这听起来像是应该在math.stackoverflow.com上提出的，但这是我从高中时代就已经忘记的尴尬简单的数学，而不是高级的研究生课程！

b
$ b

我正在做一些图形编程，而且我有一个三角形。顺便提一句，这个三角形的两边是平等的，但我不确定这是否相关。我有两个角（顶点）的坐标，但不是第三个（这些坐标是屏幕上的像素，以防相关）。我知道所有三面的长度。

我如何确定未知顶点的坐标？

其中a， b，c是边的长度（不论长度）
和A，B，C是与相同字母的边相反的角度。

使用上面的方法计算出你知道的一个端点的角度，然后使用角度，顶点的位置以及相邻边之间的角度来确定未知顶点的位置。

问题的复杂性并不能决定它应该继续进行哪一个网站，而仅仅是主题。所以你应该把它算到数学上。

OK, I know this sounds like it should be asked on math.stackoverflow.com, but this is embarrassingly simple maths that I've forgotten from high-school, rather than advanced post-graduate stuff!

I'm doing some graphics programming, and I have a triangle. Incidentally, two of this triangle's sides are equal, but I'm not sure if that's relevant. I have the coordinates of two of the corners (vertices), but not the third (these coordinates are pixels on the screen, in case that's relevant). I know the lengths of all three sides.

How do I determine the coordinates of the unknown vertex?

解决方案

for oblique triangles: c^2 = a^2 + b^2 - 2ab * cos(C)

where a, b, c are the lengths of the sides (regardless of length) and A, B, C are the angles opposite the side with the same letter.

Use the above to figure out the angle from one of the endpoints you know, then use the angle, the position of the vertex, and the angle between the adjacent sides to determine where the unknown vertex is.

And the complexity of the problem doesn't determine which site it should go on, only the subject matter. So you should move this to math.

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