Explanation:
FIRST find the hypotenuse CB
sin B = .5 = opposite leg/ hypotenuse
.5 = 3x/CB
CB = 3x/.5 = 6x
Now you can use the Pythagorean theorem
(6x)^2 = (3x)^2 + AB ^2
AB ^2 = 36x^2 - 9x^2
AB ^ 2 = 27 x^2
AB = x sqrt 27
AB = 3x sqrt 3
OR
If sin = 1/2 cos = sqrt(3) /2 Using CB = 6x as before
AB = sqrt (3)/2 * 6x = 3x sqrt 3