I will call the short side s and the hypotenuse h.
The sine rule states that in any triangle, the length of any side divided by the sine of the opposite angle is a constant.
So for your triangle we have:
8/sin 60° = s/sin 30° = h/sin 90°
8/[(sqrt 3)/2] = s/(1/2) = h/1
16/sqrt 3 = 2s = h
So the length of the short leg s
= 8/sqrt 3 = approx. 4.619
and the length of the hypotenuse
= 16/sqrt 3 = approx. 9.238.
