Measure of an angle in space

### 27.10.9 Measure of an angle in space

See Section 26.13.4 for angle measures in 2D 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
| ⎞ ⎟ ⎟ ⎠