AC9M9SP01

recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity

Elaborations

AC9M9SP01_E1 - 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
AC9M9SP01_E2 - 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
AC9M9SP01_E3 - 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
AC9M9SP01_E4 - 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

Achievement Standard Components

ASMAT911 - Students apply Pythagoras’ theorem and use trigonometric ratios to solve problems involving right-angled triangles.
ASMAT912 - They use mathematical modelling to solve practical problems involving direct proportion, ratio and scale, evaluating the model and communicating their methods and findings.