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:
c^{2} = a^{2} + b^{2} - 2abcosC
which can also be written as:
a^{2} = b^{2}+ c^{2} - 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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