GM5-10: Apply trigonometric ratios and Pythagoras' theorem in two dimensions.

Elaboration on this Achievement Objective

This means that students will apply trigonometric ratios to find the angles and lengths of sides in right-angled triangles. Students need to recognise two features of trigonometric ratios:

  1. Given similar right angled triangles the ratios of side lengths are the same, for example 
    similar triangles.

For both triangles the ratio of the sides opposite and adjacent to angle A is 6/8 = 0.75. For any similar triangle this is also true. This ratio is the tangent of angle A, so A = 37°.

  1. The trigonometric ratios can be found using a right-angled triangle with a hypotenuse of one and applied to any other similar right angled triangle by scaling.

The trigonometric ratios are:

  • sin θ = side opposite θ/hypotenuse,
  • cos θ = side adjacent to θ/hypotenuse,
  • tan θ = side opposite θ/side adjacent to θ

These ratios are often remembered using the mnemonic SOH CAH TOA.

Students will use Pythagoras’ theorem (a2 + b2 = c2) to find the lengths of sides of right angle triangles.

Pythagoras' theorem.