Lesson 25 Triangle ratios

# Triangle ratios

Overview Resources
An activity exploring the concepts of trigonometric ratios, leading to an understanding of them as functions. Only tangent and sine are handled, firmly based on pupils’ own geometric constructions. Drawings, measurements and calculations are used, but accuracy is not emphasised. The focus is on the coordination of relations inside the triangle and between triangles. A set of similar right- angled triangles made from different coloured paper (see page 200). Blu-tack. Worksheets 1 and 2
Protractors. Rulers. Calculators
Ratio and proportion in geometric contexts.
• Interpret and use ratio in a range of contexts,
• Recognise that enlargements preserve angle but not length<
• Know that if two 2-D shapes are similar, corresponding angles are equal
and corresponding sides are in the same ratio,
• Begin to use sine and tangent in right-angled triangles.
• EPISODE 1
Similar triangles and their properties
Pupils as a class explore properties of similar triangles using cut-out similar triangles of different sizes superimposed on each other. They clarify the meaning of similar triangles and corresponding sides, and recognise the need for clear labelling of sides in relation to the right angle.
EPISODE 2
Exploring the tangent of angles between 0° and 90°
Pupils are given different angles and by drawing a series of right-angled triangles and measuring they calculate a value for the tangent of that angle and the sine ratio. Accuracy in measuring angles and lengths are not emphasised.

Their findings are then brought together in a simple list or table and the range of values for the tangent is discussed, extended to cases where the angle is nearer to 0° or 90°, Calculator values are compared with their experimental results.
EPISODE 3
Exploring the sine ratio in right-angles triangles
Pupils find the sine ratios for the triangles they have drawn and their findings are brought together in a table. They discuss the range of values for sine, comparing it with that for the tangent, and with calculator values.