To sine or to cosine

To sine or to cosine? That is the question. Choosing the correct rule to use to solve problems in non right-angled triangles

Given 2 sides and an included angle A

 To find a side: Use the Cosine rule

c B

b

 To find an angle: Use the Sine rule C

 To find the third angle: Use basic geometry!

a

Given 2 angles and a side  To find a side: Use the sine rule  To find the third angle: Use basic geometry.

Given 3 sides  To find the first angle Use the Cosine rule  To find second angle Use the Sine rule  To find the third angle Basic geometry!

Given 2 sides and a nonincluded angle  The ambiguous case…..

 To find 2 possible angle values: Use the sine rule  To find 2 possible side values Use the sine rule

If all else fails…..  Use the sine rule – it’s easier!

 But if it doesn’t work, then it must be the cosine rule you need.