Finding the angle between a line and a plane

To find the angle between the line PQ and the plane ABCD:

1. Draw a line from Q which is perpendicular to the plane ABCD and meets the plane at X.
2. Join X to P.

Click 'Go' in the diagram to show the lines QX and QP:

We now have a right-angled triangle, so we can use trigonometry. The angle between PQ and the plane ABCD is the angle we have to find.

This method can be applied to all three-dimensional (3-D) problems.

A cuboid

Click 'Go' to reveal the angle between the diagonal AG and the base of the cuboid ABCD:

A square-based pyramid

Click 'Go' to reveal the angle between PV and the base PQRS: