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

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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.