Right ABC has its right angle at C, BC=4 , and AC=8 .

First find the length of the hypotenuse using pythagorean theorem       c²  = a²+b²

^{then draw the triangle}

sin a  =  opposite / hypotenuse        where ' opposite'   is the side leg that is opposite angle A

sin A  =   BC / BA

We  need  to  find BA.....this is  = √[8^2 + 4^2 ]  = √80  =  4√5

So

sin A  =  4 / [ 4√5]  =   1  / √5

Rationalizing the denominator we  have   sin A  =   √5 / 5