In a right-angled triangle, angle c = 90 degrees, sin of angle B = 0.8 find AB, AC.

These conditions are not enough to find the required sides of a right-angled triangle. We express the sought AB and AC in terms of BC.
The sine of an acute angle of a right-angled triangle is the ratio of the leg opposite this angle to the hypotenuse: sin∠B = AC / AB.
We have: sin∠B = AC / AB = 0.8, whence AC = 0.8 * AB.
By the Pythagorean theorem, AC ^ 2 + BC ^ 2 = AB ^ 2.
Therefore, BC ^ 2 = AB ^ 2 – (0.8 * AB) ^ 2 = 0.36 * AB ^ 2, i.e. AB = (5/3) * BC.
Then, AC = (4/5) * (5/3) * BC = (4/3) * BC.
Answer: AB = (5/3) * BC; AC = (4/3) * BC.