The formula for finding the line-plane angle is cosθ=a*b/(|a|*|b|).

Not parallel to the plane of the line on a point for the plane of the vertical line, this vertical line and the plane of the intersection of the original line and the plane of the intersection of the line and the original straight line constitutes (the line and the original angle of the angle of the residual angle) that is, for the line angle.

The upper part of the formula: the coordinate operation of the product of quantities of a and b: let a = (x1, y1), b = (x2, y2), then a - b = x1x2 + y1y2. The lower part of the formula is the product of the modes of a and b: let a = (x1, y1), b = (x2, y2), then (|a||b|) = (x1 squared + y1 squared) * (x2 squared + y2 squared) under the root sign.

Methods for solving line-line and line-plane angles

Line-line angles can be obtained directly by using the formula because the range of line-line angles is (0,π/2], so the sine and cosine of their angles are both constant greater than or equal to zero, so it is sufficient to directly find the absolute value.

The line angle is obtained with the help of the normal vector of the plane, the line angle is reciprocal to the angle formed by the normal vector of the line and the plane, so the sine of the line angle is the cosine of the angle formed by the normal vector of the line and the plane, the cosine of the line angle is the sine of the angle formed by the normal vector of the plane.

And because the range of the line-plane angle is also (0,π/2], the sine and cosine of the angle are always greater than or equal to zero, so the cosine of the angle between the line and the normal vector of the plane can be taken as the absolute value.