How can the line down the middle of an equilateral triangle be calculated using the sine rule?

To prove the Sine rule first draw a line down the middle of a triangle and label it x and identify the sides that are not divided – b is cut down the middle, while a and c are hypotenuses’. This makes x the opposite of the hypotenuses’, so Sinx = o/h is used. Now substitute a and c into the equation to get SinA = x/c and SinC = x/a. Rearrange these equations to remove the fractions by multiplying by c or a to get cSinA = x and aSinC = x. Which becomes = cSinA = aSinC. And finally, divide the equation on the left by SinA and on the right by SinC so it becomes c/SinC = a/SinA and is now the sine equation.