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Cosine RuleCosine RuleAnglesAngles

Stage 6 - Year 12Stage 6 - Year 12

General Mathematic(HSC)

2

The Cosine Rule – Find an Angle (1/2)

AA

aa

BB

bb

CC

cc

Cos C =a2 + b2 – c2

2ab

Cos B =a2 + c2 – b2

2ac

Cos A =b2 + c2 – a2

2bc

To use the Cosine Rule – Angle we need …three sides

Cos-1( )2x7x5

2x7x5

3

The Cosine Rule – Find an Angle (2/2)

AA

77

BB

55

CCoo

66Cos C =a2 + b2 – c2

2ab

Cos C = + 5272 – 62

Cos C = + 5272 – 62Cos-1

C = 57.12165044o

C ≈ 57o