Sine Rule

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The sine rule is a trigonometric rule which is true for all triangles.

The sine rule states that, in the above triangle abc:

SinA = SinB = SinC

a b c

This rule is very useful if you know 3 pieces of information about a triangle, and need to find a fourth. For example:

To find x, we can use the sine rule:

Sin(x) = Sin54

4 9

Sin(x) = 4Sin54

9

Sin(x) = 0.3596

x = 21.073

There are 2 conditions necessary for the sine rule to be useful:

We must know at least 3 pieces of information (sides/angles).

We must know at least 1 corresponding side/angle pair*.

*e.g if we know angle A, side length b and angle C, the sine rule won't help us.

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