Sine and Cosine Rule

The Sine Rule

The sine rule is an important rule relating the sides and angles of any triangle (it doesn't have to be right-angled!):

If a, b and c are the lengths of the sides opposite the angles A, B and C in a triangle, then:

Image

  a  

=

  b  

=

  c  

sinA   sinB   sinC


If you wanted to find an angle, you can write this as:

sinA

=

sinB

=

sinC

a

 

b

 

c

The Cosine Rule

This also works in any triangle:

c2 = a2 + b2 - 2abcosC

which can also be written as:

a2 = b2+ c2 - 2bccosA

The area of a triangle

The area of any triangle is ½absinC (using the above notation).

This formula is useful if you don't know the height of a triangle (since you need to know the height for ½ base × height).

 

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