In a right-angled triangle ABC, legs AC-16, BC = 12 are known. Find sin B.

To begin with, using the Pythagorean theorem, we find the length of the hypotenuse AB of a given right-angled triangle.

In the initial data for this task, it is reported that the length of the AC leg of this triangle is 16, and the length of the BC leg is 12, therefore, the length of the hypotenuse AB is:

| AB | = √ (| AC | ^ 2 + | BC | ^ 2) = √ (16 ^ 2 + 12 ^ 2) = √ (256 + 144) = √400 = 20.

Now, applying the sine theorem, we find sin (B):

| AB | / sin (90 °) = | AC | / sin (B);

sin (B) = (| AC | / | AB |) * sin (90 °) = 16/20 = 4/5 = 0.8.

Answer: sin (B) = 0.8.