I have a triangle , coordinates of two vertices are known [(x1,y1,z1) and (x2,y2,z2)] . I know all the side lengths and angles of the triangle. I want to find the coordinates (x3,y3,z3) of 3rd vertex.
Hope I will get a solution from Math Help Forum.
I have a triangle, coordinates of two vertices are known: . and
I know all the side lengths and angles of the triangle.
I want to find the coordinates of 3rd vertex.
undefined is absolutely correct!
Let the sides be and the angles
Place on the "floor"
Code:* - - - - - - - - - - - - - - - - * / B / / ..o. / / ..*:::β:*. / / ..*:::::::::::*. / / ..*:α:::::::::::::::*. / / o'''*'''*'''*'''*'''*'''o C / / A / * - - - - - - - - - - - - - - - - *
Then vertex can be revolved about to any position .
Code:C' o-- ----*-- *--------*-- -------------*- B *---------------..o. -----------..*::β::*. *------..*:::::::::::*. --..*:α:::::::::::::::*. o'''*'''*'''*'''*'''*'''o C A
Therefore, there are a brizillion locations for point
Hello Thanks for the useful diagrams and solutions.
I have some more informations.
1) The Triangle is on a sphere whose center and Radius is known.
2) One end point of triangle is center of sphere ie, (0,0,0)
3) Second end point also I have.
4) I have to find the third end point.
5) I have a line that is perpendicular to one side of triangle, connecting the unknown vertex and (0,0,0) vertex. So using the direction cosines l1l2+m1m2+n1n2=0 property, I can check out of all vertices which is the valid vertex.
So I would like to know the method of finding the third vertex (eventhough infinite many solutions) from the available sides and angles and two vertices known,also the triangle is on a sphere .
And for example "3) Second end point also I have." This is vague and doesn't really help us answer your question. If you have it, why don't you tell us what it is?
Actually, this is not a text book problem. I am doing Space research for my Mtech programme. Sorry for the inconvenience caused. Since it is space Research related and I don't have the coordinates as such. If I have proper method only I can go for simulation. I am just designing the concept now. The Sphere is nothing but Earth. The Problem which I have mentioned here is part of the Global Problem. Yah what you said is right, Spherical Geometry can also be considered here. A triangle on the sphere relates to Spherical geometry, I read somewhere. But we cannot consider normal triangle on a sphere? I have put only the Geometry problem in this forum. For the time being I can ignore the sphere part. Can I get the method to find the third vertex. I am Sorry once again. So I will state my problem clearly: 1) I have a triangle whose all sides and angles are known. 2) Two vertices are known. 3) There is a line whose direction cosines are known, which is perpendicular to one side of triangle having unknown vertex and one known vertex. 4)I require to find the third vertex. Thank you friends.