3D trigonometry: angle between a line and a plane

Change the length, width and height of a cuboid or pyramid. The right-angled triangle you need is shaded and the working is shown.

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Questions students ask

How do you find the angle between a line and a plane?

Drop a perpendicular from the line to the plane to make a right-angled triangle, then use trigonometry (usually tan) on that triangle.

How long is the space diagonal of a cuboid?

√(l² + w² + h²), from using Pythagoras twice.

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