Sine Rule

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Note by , created almost 6 years ago

This note explains what the sine rule is and how it can be used

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Created by rory.examtime almost 6 years ago
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Page 1

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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