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Sine rule

The sine rule is

 


Explanation

In a triangle, you can describe the sine of any angle easily using the altitudes. With the altitude from angle A you can express the sine of DB and DC as

and

It follows that

and you can write it as

Now we take the altitude from angle B, and find

and

It follows that

and you can write this as

Now we take the altitude from angle C, and find

and

It follows that

and you can write this as

All this gives

 


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