MA30-10 Maths Coming soon
Finding the angle between a line and a plane
MA30-10
This lesson is coming soon.
In this lesson
Construct and find the angle between a line and a plane in a 3D solid, by identifying the point where the line meets the plane and the foot of the perpendicular from the line's other end onto that plane.
What it covers
- Understand that the angle between a line and a plane is measured at the point where the line meets the plane, using the line's projection onto that plane
- Construct (draw onto the diagram) the perpendicular from a point on the line down to the plane, creating the right-angled triangle needed
- Identify the correct right-angled triangle formed by the line, its projection onto the plane, and the perpendicular, then use trigonometry to find the angle
- Apply this to a standard solid such as a cuboid (angle between a space diagonal and the base) or a pyramid (angle between a sloping edge and the base)
Key words
For: Cambridge IGCSE 0580, Edexcel IGCSE 4MA1
On the specification
| Board | Spec | Statement |
|---|---|---|
| Cambridge IGCSE 0580 | C6.6 | Extended content only. |
| Cambridge IGCSE 0580 | E6.6 | Carry out calculations and solve problems in three dimensions using Pythagoras' theorem and trigonometry, including calculating the angle between a line and a plane. |
| Edexcel IGCSE 4MA1 | H4.8F | Apply trigonometrical methods to solve problems in three dimensions, including finding the angle between a line and a plane |
For teachers
This GCSE Maths lesson teaches finding the angle between a line and a plane. By the end, students should be able to construct and find the angle between a line and a plane in a 3D solid, by identifying the point where the line meets the plane and the foot of the perpendicular from the line's other end onto that plane. It works through two worked examples and the mistakes examiners report.