AC9M9SP01

Elaborations

• AC9M9SP01_E1understanding 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
• AC9M9SP01_E2investigating 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
• AC9M9SP01_E3establishing 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
• AC9M9SP01_E4relating 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