Achievement objective GM66
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
 use trigonometric ratios and Pythagoras’ theorem in two and three dimensions.
Indicators
 Solves problems that can be modelled with right angle triangles.
 Uses trigonometric ratios to find lengths and angles in 2 and 3dimensions.
 Uses Pythagoras’ theorem to find lengths in 2 and 3dimensions.
 See
key mathematical ideas on NZmaths.
Progression
GM66 links to
M74.
Possible context elaborations
 The problems should involve finding either an unknown length or angle.
 For example, find the angle ABC and the length of the line BC.
If you cannot view or read this diagram,
open this text version.
 Problems with points described using coordinates.
 Shows triangles are rightangled.

Julie’s wheels using Pythagoras’ theorem to find the size of a wheel.

Height of the school: Using at least three different methods

Making a box the shape of a pyramid: Exploring angles in a 3D shape, connects to measurement.
 Use trigonometric ratios and Pythagoras to find bearings.
Assessment for qualifications
NCEA achievement standards at level 1, 2 and 3 have been aligned to the New Zealand Curriculum. Please ensure that you are using the correct version of the standards by going to the
NZQA website.
The following achievement standard(s) could assess learning outcomes from this AO.
Last updated September 16, 2018
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