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NZAMT NZQA NZ Grapher NZ Maths Census at School Study It

AS 1.7 Triangles Home AS91032

Triangles home | Pythagoras A | Calculator Practice | Trig Finding Sides | Trig Finding Angles | Trig Applications | Vectors | Bearings | 1.7 Revision

For Teachers

* Be familiar with the Achievement Standard 1.7 #91032 (link to NZQA)

* Assessment resources on TKI 1.7 Av2 (Word) | 1.7 Bv2 | 1.7 C

* Link to NZQA resources with worked examples and explanation 1.7 B

* NZQA Clarifications page

* Check the latest comments on the NZmaths forum (login required)

* Any further ideas / suggestions / resources/ comments / errors. Please email

* AS 1.7 section on Nayland Web site updated: July 2013


AS 1.7 Triangles AS91032 (3 credit internally assessed)

AS 1.7 Apply right-angled triangles in solving measurement problems basically involves making some practical measurements then using Pythagoras & Trigonometry to solve problems

Useful Homework Book:



Possible Lesson Sequence for 1.7 Probability Methods AS91267

1. Basic


Applications of Pythagoras

Properties of triangles Trig introduction

Trig: finding side lengths

Trig: finding angles Applications

3D Applications A

3D Applications B

Vectors + - × ÷<

Vectors & Bearings

Grid references






Using pythagoras in 2 and 3 dimensions.
Using trigonometry in 2 and 3 dimension

- Use trigonometric ratios and Pythagoras’ Theorem in two and three dimensions.
- Recognise when shapes are similar and use proportional reasoning to find an unknown length.
- Select and use appropriate metric units for length and area.
- Measure at a level of precision appropriate to the task.

For this standard students need to take their own measurements to solve problems.


AS 1.7 involves Pythagoras and trigonometry involve RIGHT angle triangles.

Trigonometry is used on a daily basis in the workplace.  Since trigonometry means "triangle measure", any profession that deals with measurement deals with trigonometry as well.  Builders, construction workers and engineers, for example, must possess a thorough understanding of trigonometry.  

Pythagoras involves the 3 SIDES of a right angle triangle

               a2 + b2 = c2

Trigonometry involves 2 sides & 1 ANGLE in a right angle triangle

             SOH CAH TOA


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