Topic 29 - Sine and cosine rules

Module 29 of 32

Contents: Sine and cosine rules

Time: 4 – 6 hours

SPECIFICATION REFERENCE

GM h

GM y

Use the sine and cosine rules to solve 2-D and 3-D problems

Calculate the area of a triangle using absinC

PRIOR KNOWLEDGE

· Trigonometry

· Formulae

OBJECTIVES Lesson plans

· Calculate the unknown lengths, or angles, in non right-angle triangles using the

sine and cosine rules (29.5–29.9)

· Calculate the area of triangles given two lengths and an included angle (29.4)

DIFFERENTIATION & EXTENSION

· Use these ratios to solve problems in 3-D and decide if it is easier to extract right-angle triangles to use

‘normal’ trigonometry

· Stress that the cosine rule is only used when we have SAS (and we need to find the side opposite the angle

given) or when we are given SSS (then we use the re-arranged version to find any angle) [else we use the

Sine Rule]

NOTES

· Reminders of simple geometrical facts may be helpful, eg angle sum of a triangle, the shortest side is

opposite the smallest angle

· Show the form of the cosine rule in the formula page and re-arrange it to show the form which finds missing

angles