In a right-angled triangle ABC, the hypotenuse is 12 and the sine of angle A is 2/3. Find the leg opposite corner A.

It is known that in a right-angled triangle the sine of an angle is the ratio of the opposite leg to its hypotenuse.

Thus, we obtain that CB / AB = sin A;

This means that the unknown leg CB will be equal to AB * sin A;

Thus, we get the final solution to our problem:

CB = AB * sin A

Substitute the values from the condition and get the final answer:

CB = 12 * 2/3;

CB = 24/3;

CB = 8 cm.

Thus, we found the leg opposite to the angle A: CB equal to 8 cm.

Answer: 8 cm.