From some point to the plane, a perpendicular and an inclined line are drawn, the angle between which is 30 °

From some point to the plane, a perpendicular and an inclined line are drawn, the angle between which is 30 °. Find: a) the perpendicular if the slope is 16 cm; b) the angle between the inclined and the plane.

AC is perpendicular to the α plane, segment BC is the projection of the inclined AB onto the α plane.

Since BC belongs to the plane α, BC is perpendicular to AC, and then triangle ABC is rectangular.

In a right-angled triangle ABC CosBAC = AC / AB.

AC = AB * Cos30 = 16 * √3 / 2 = 8 * √3 cm.

The angle between AB and the plane α is the linear angle ABC between the inclined AB and its projection onto the plane

Angle ABC = (90 – 30) = 60.

Answer: The perpendicular is 8 * √3 cm, the angle between the inclined and the plane is 60.