Proof of Law of Sine

The Law of Sine

The Law of Sine states that given any triangle with side lengths a, b and c and opposing angles A, B and C

First we'll divide the triangle into two right triangles by drawing the line that passes through A and is perpendicular to a 

From the definition of sine ;

or 

Since both are equal to h ; we can say that :

Now dividing by sinB and sinC , gives us ;

Hence Proved ! 

Now you give it a try it for other sides and ratios to further prove !