The measure of an angle in space: angle

### 14.12.9 The measure of an angle in space: angle

See Section 13.14.4 for angle measures in two-dimensional geometry.

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

Three points.

- angle takes three arguments:
  A,B,C, three points.
- angle(A,B,C) returns the measure of the undirected angle BAC.

#### Example.

Input:

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

Output:

1
2
| π

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.

#### Example.

Input:

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

Output:

arccos | ⎛ ⎜ ⎜ ⎝ |
√ |
6
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.

#### Example.

Input:

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

Output:

arccos | ⎛ ⎜ ⎜ ⎝ |
√ |
6
3
| ⎞ ⎟ ⎟ ⎠