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To use the Sine Rule
You need one complete ratio (Side to its opposite angle)
a/sinA = b/sinB = c/sinC OR sinA/a = sinB/b = sinC/c
This is used to find either a side or an angle in a non right-angled triangle. This is the Sine Rule. You do not need to use all three ratios, just one that you know and the one that you need to complete.
To use the Cosine Rule
You need to have two sides and the included angle
This is the equation for the Cosine Rule, it can be changed to have b or c as the subject (e.g. b²=a²+c²-2ac(cos)B).
You should use the Sine and/or Cosine Rule
When the triangle is non right-angled
You should use SOHCAHTOA
When the triangle is right-angled