Te reo Māori terms
click each term to open in Te Aka
Learning objective overview
Master Teaching Guide coverage for this objective.
Current NZC (2007)
GM6-6
New NZC (2026)
NZC26-P4-MEA-MEA-P-Y10-10
Resources
- CorbettMaths on 3d Pythagoras’ TheoryQuestions PDF · Answers
- CorbettMaths on using trigonometry to solve for unknown sidesQuestions PDF · Answers
Terminology
- space diagonal
- face diagonal
- cuboid
- 3D shape
- Pythagoras' theorem
- trigonometric ratio
- sine
- cosine
- tangent
- angle to the base
Task goals
- Find face diagonals of rectangular faces in 3D shapes using Pythagoras' theorem.
- Calculate space diagonals of cuboids using a two-step method combining Pythagoras applications.
- Use trigonometric ratios (sine, cosine, tangent) to find heights or angles when given a sloping line and one other measurement.
- Solve multi-step 3D problems that require both Pythagoras' theorem and trigonometry to reach the final answer.
- Identify which right triangle to use in a 3D context and determine whether the angle is measured from the base or vertical.
- Justify solutions using both exact values and decimal approximations, recognising when early rounding affects the final answer.
Where this fits
What leads into this objective, and where it goes next.
Before
Multi-step Pythagoras' theory
Perimeter of compound shapes using Pythagoras' theory
Mixed revision of Pythagoras' theory
You are here
Applying Pythagoras’ theory and trigonometry to 3D shapes
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.