the sine of an angle given as a ratio is expressed as the length of the side opposite to the angle (that is straight ahead) divided by the length of the hypotenuse(the longest side).

so in this example, sinA = BC/AB = 5/AB

but we don't know the length of AB, not yet. we will use pythagoras' theorem to find it. pythagoras' theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. so if a is the hypotenuse, and b and c the other two sides, then we have:

a^2 = b^2 + c^2

similarly, for this question, we have:

(AB)^2 = (BC)^2 + (AC)^2

=> (AB)^2 = 5^2 + 12^2

=> (AB)^2 = 169

=> AB = sqrt(169)

=> AB = 13

so now, sinA = 5/13 = 0.3846 to four decimal places