shape & space : Sin & Cosine Rules
 

 

the Sine Rule

  

 

 

 

The Sine Rule

 

sine rule

 

    1. Use either the right, or left hand equation.
    2. You are given 3 quantities and required to work out the 4 th.

 

Manipulating the ratio - Take two ratios, cross multiply and rearrange to put the required quantity as the subject of the equation.

 

      sine rule derivatives

 

Example #1

sine rule prob#1

 

sine rule prob#1

 

Example #2

sine rule probs #2

 

sine rule prob #2

 

Example #3

sin rule probs #3

 

sine rule prob#3

 

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The Cosine Rule

 

cosine rule

 

There are two problem types:

  1. You are given 2 sides + an included angle and required to work out the remaining side
  2. You are given all the sides and required to work out the angle.

 

Example #1

cosine rule prob #1

 

cosine rule prob #1

 

Example #2

cosine rule prob#3

 

cosine rule prob #2

 

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