A segment with a length of 10 cm intersects the plane, its ends are respectively at a distance of 3

A segment with a length of 10 cm intersects the plane, its ends are respectively at a distance of 3 and 2 cm from the plane, find the angle between this segment and the plane.

The shortest distance from a point to a plane is the perpendicular. If we continue the perpendiculars dropped from the ends of the segment to the plane, then we get a right-angled triangle, one of the legs of which is parallel to the plane, and the other is perpendicular.

The angle formed by the segment and the plane is equal to the angle formed by the hypotenuse and the leg parallel to the plane, since they are internal crosswise.

Therefore, the sine of the angle formed by the segment and the plane is equal to the ratio of the sums of the distances from the ends of the segment to the plane to the length of this segment:

sin α = (2 + 3) / 10 = 5/10 = 0.5.

According to the table of sines and cosines, this corresponds to an angle of 30 °.

Answer: the angle formed by the line segment and the plane is 30 °.