Title

Sine and Cosine Rule
Quick revise

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:
Triangle

  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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