AC9M9SP01
Year 9
Mathematics
AC9M9SP01 | Year 9 Mathematics: Space
Content Descriptor
Content descriptor recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity
Strand
Space
Substrand
Space
This content descriptor sets out learning for Year 9 Mathematics. Use it to plan lessons and assessment with the Australian Curriculum v9.
Elaborations
- • Elaboration understanding the terms “base”, “altitude”, “hypotenuse”, and “adjacent” and “opposite” sides to an angle, in a right-angled triangle, and identifying these for a given right-angled triangle
- • Elaboration investigating patterns to reason about nested similar triangles that are aligned on a coordinate plane, connecting ideas of parallel sides and identifying the constancy of ratios of corresponding sides for a given angle
- • Elaboration establishing an understanding that the sine of an angle can be considered as the length of the altitude of a right-angled triangle with a hypotenuse of length one unit and similarly the cosine as the length of the base of the same triangle, and relating this to enlargement and similar triangles
- • Elaboration relating the tangent of an angle to the altitude and base of nested similar right-angled triangles, and connecting the tangent of the angle at which the graph of a straight line meets the positive direction of the horizontal coordinate axis to the gradient of the straight line
Plan a lesson from this content description.
Start freeAchievement standard statements this supports
- Students apply Pythagoras’ theorem and use trigonometric ratios to solve problems involving right-angled triangles.See it on the standard page →
- They use mathematical modelling to solve practical problems involving direct proportion, ratio and scale, evaluating the model and communicating their methods and findings.See it on the standard page →