Suppose a line intersects a plane at one point. Define what is meant by the "angle of intersection of the line

Question

Suppose a line intersects a plane at one point. Define what is meant by the "angle of intersection of the line and the plane". Describe a method you can use to determine the angle of intersection of a line and a plane.

Answer 1

Suppose another plane include the line and perpendicular to the plane. The angle between the line and the new line that determine of intersecting two plane is the angle between the line and the plane and this is the method for finding this angle:

You should find the angle (90-A) which A=the angle between the line and the normal vector of plane
CosA=B.N/|B|.|N|

Answer 2

Suppose the line intersects the plane at point P. Pick another arbitrary point on the line Q. Construct a line thru Q that is normal to the plane. The normal line will intersect the plane at point which we will call R. Now we have a triangle QPR. The angle QPR is defined as the angle of the line to the plane.