How would I go about it?
figuring out the x,y, and z rotation of a right triangle?
0
$\begingroup$
geometry
trigonometry
-
2Your question is too vague... – 2010-12-06
-
0It is not clear what the question is, nor what data is available for the solution. Do you want to bring a right triangle into some standard position? Or find what the angles at the vertices are? Or what? – 2010-12-06
-
0How can I make it less vague? – 2010-12-06
-
0I have a triangle made of 3 vertices. I need to know what the angle of the triangle is. – 2010-12-06
-
0Triangles generally have three vertices, and three angles. – 2010-12-06
-
0Yes, and I need all three angles. – 2010-12-06
1 Answers
0
So you have the co-ordinates $P_i = (x_i, y_i, z_i), \ \ i=1,2,3$ of the vertices and you want to find the angles of the triangle formed by $P_1, P_2, P_3$?
Let the angle at $P_1$ be $\theta_1$.
If
$\displaystyle \vec{a} = (x_3 -x_1, y_3 - y_1, z_3 - z_1)$
$\displaystyle \vec{b} = (x_2 - x_1, y_2 - y_1, z_2 -z_1)$
The we have that
$\displaystyle |\vec{a}| |\vec{b} | \cos \theta_1 = \vec{a} \cdot \vec{b}$
Where $|\vec{v}|$ is the length of $\vec{v}$ and $\cdot $ is the dot product.
Similarly, you can find the other angles.
For more information, see here: Understanding the Dot Product.
-
0Extra credit-this does not require that the triangle be right. – 2010-12-07