Hi, In 2D, we can express the sides of a right angle triangle with sines and cosines. Is there a way to extend this idea to 3D? I.E. i have a right angle triangle with sides A and B, with magnitude of and angle . Is there a similar analysis that can be applied to something that has a 3rd dimension? i.e. with magnitude of
Triangles are by definition 2D. You are wanting to deal with a pyramid if you use 3D. Could you draw what you are trying to describe?
well essentially i have something with magnitude . I want do be able to break this down into terms of sine and cosine, which usually only applies to 2d right angle triangles. For example, for I can easily form a triangle with hypotenuse of that and sides with length A and B. Then i can use sin and cosine to describe or quite easily. However, I am wondering if there is a similar approach or method that can be applied to geometries with magnitudes of hope that makes my question more clear
If you have a rectangular box with sides of length A, B, and C, then the length of the diagonal is . You should try to derive this for yourself. Start with any two sides (which line in a plane) and find the hypotenuse. This is the diagonal of that side. Now use that hypotenuse and the thrid side (which again define a plane) and find the hypotenuse of that. This IS the diagonal of the rectangular solid.