In a right-angled triangle ABC with a right angle C sin A = 0.8. Find the sine B.

sin A = BC / AB = 0.8 (1) (ratio of the opposite side angle to the hypotenuse)
Whence BC = 0.8 * AB (2)
Using the Pythagorean theorem for right-angled triangles, we can write:
AC ^ 2 + BC ^ 2 = AB ^ 2 (3)
We make a substitution from relation (2).
AC ^ 2 + 0.64 AB ^ 2 = AB ^ 2 (4)
AC ^ 2 = 0.36 * AB ^ 2 (5)
We extract the root from both parts:
AC = 0.6 * AB (6)
A-priory
sin B = AC / AB
We substitute the found expression in (6) instead of AC
sin B = (0.6 * AB) / AB = 0.6
Answer: 0.6