Te reo Māori terms
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Learning objective overview
Master Teaching Guide coverage for this objective.
Current NZC (2007)
GM6-6
New NZC (2026)
NZC26-P4-GEO-SHP-P-Y10-01
Resources
- CorbettMaths - 3D Trigonometry
- CorbettMaths - 3D Trigonometry: Practice Questions
- CorbettMaths - 3D Trigonometry: Textbook ExerciseQuestions PDF · Answers
Terminology
- Angle between a line and a plane
- Projection onto a plane
- Space diagonal
- Right-angled triangle within a solid
- Angle between two planes
- Base diagonal
- Foot of the perpendicular
Task goals
- Foundation: Identify right-angled triangles hidden within simple 3D solids such as cuboids and pyramids, and use Pythagoras' theorem to find an unknown edge or diagonal length.
- Proficient: Construct the projection of a line onto a plane within a 3D solid and use trigonometric ratios to calculate the angle between the line and that plane.
- Excellence: Solve multi-step problems requiring the angle between two intersecting planes of a solid, combining Pythagoras' theorem and trigonometric ratios across more than one constructed right triangle.
Where this fits
What leads into this objective, and where it goes next.
Before
Applications of Trigonometric Ratios: Finding Angles
Introduction to Trigonometry: Finding an Angle
Applications of Trigonometric Ratios: Finding Lengths
You are here
Angles Between Lines and Planes in 3D Solids
Next
Year 10 is the last year of this phase — the curriculum lists nothing after this. No extension resources on the site yet.
Also under GM6-6:
For teachers
Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.