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Learning objective overview
Master Teaching Guide coverage for this objective.
Current NZC (2007)
GM5-10
New NZC (2026)
NZC26-P4-GEO-SHP-P-Y10-01
Resources
- CorbettMaths on using trigonometry to solve for unknown sidesQuestions PDF · Answers
- Beta: Exercise 22.01, pg 422
- Beta: Exercise 22.13, pg 441
- Beta: Exercise 22.14, pg 442
- Beta: Parallel Skills Exercise 22C, pgs 442 & 443
- Beta: Application: Ex 23.03, pgs 448 & 449
Terminology
- trigonometry
- trigonometry ratio
- right-angle triangle
- hypotenuse
- adjacent
- opposite
- soh cah toa
Task goals
- Label the hypotenuse, adjacent, and opposite sides of a right-angled triangle relative to a given angle.
- Choose and apply the correct trigonometric ratio (sine, cosine, or tangent) to find a missing side length given an angle and one other side length.
- Find a missing side length from a labelled diagram giving an angle and one side length of a right-angled triangle.
- Round a calculated length to one or two decimal places, as instructed.
- Solve a real-world worded problem (such as a ladder, ramp, kite string, tree shadow, or building) by finding an unknown height, distance, or length using a given angle.
- Find two unknown side lengths of the same right-angled triangle from a single given angle and side length.
- Solve a multi-step problem that combines finding a length with finding an angle, or that involves the triangle's dimensions changing (for example, moving the observation or anchor point) and recalculating.
Where this fits
What leads into this objective, and where it goes next.
You are here
Applications of Trigonometric Ratios: Finding Lengths
Do
Using the properties of similarity in 2D shapes, including right-angled triangles, to find unknown lengths and angles
Statement▸
Year 10 · Geometry · Shapes
NZC26-P4-GEO-SHP-P-Y10-01
Next
Year 10 is the last year of this phase — the curriculum lists nothing after this. Extension resources: Trigonometric Ratios: Finding a Side, Using the Sine Rule to find missing sides.
Also under GM5-10:
For teachers
Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.