Measure of an angle in space

### 25.10.9 Measure of an angle in space

See Section 24.13.4 for angle measures in two-dimensional geometry.

The angle command finds the measures of angles in space. It can take its arguments in three different ways.

1. Three points.
   - angle takes three arguments: A,B,C, three points.
   - angle(A,B,C) returns the measure of the undirected angle BAC.
2. Two intersecting lines.
   - angle takes two arguments: L,M, two lines which intersect.
   - angle(L,M) returns the measure of the angle between the lines L and M.
3. A line and a plane.
   - angle takes two arguments:
     - L, a line.
     - P, a plane.
   - angle(L,P) returns the measure of the angle between L and P.

#### Examples

angle(point(0,0,0),point(1,0,0),point(0,0,1))

1
2
| π

angle(line([0,0,0],[1,1,0]),line([0,0,0],[1,1,1]))

arccos | ⎛ ⎜ ⎜ ⎝ |
√ |
6
3
| ⎞ ⎟ ⎟ ⎠

angle(line([0,0,0],[1,1,0]),plane(x+y+z=0))

arccos | ⎛ ⎜ ⎜ ⎝ |
√ |
6
3
| ⎞ ⎟ ⎟ ⎠