The angle ϕ between a line with direction b and a plane with normal n satisfies

1. Let α be the angle between line direction b and plane normal n. 2. Then cos α = (b · n) / (|b| · |n|). 3. The angle between the line and the plane is ϕ = 90° - α. 4. Therefore sin ϕ = cos α = (b · n) / (|b| · |n|). _Source: NCERT Class 12 Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.10_