Here is a triangle with sides A, B and C and angles a, b and c:
Lets call the height h1 when using B as the base:
We can write h1 in two ways:
From this we know:
Now lets say that h2 is the height of the triangle when using C as the base:
We can write h2 in two ways:
From this we know:
Now we have the sine rule:
