In a right-angled triangle ABC, the sine of the angle a = 12/13, what are the legs AC and BC, if the hypotenuse = 13?

Since the sine is defined as the ratio of the opposite leg to the hypotenuse, it follows that:

sin A = CB / AB

12/13 = CB / 13

CB = 12 cm

To find AC, we use the Pythagorean theorem, according to which the square of the hypotenuse is equal to the sum of the squares of two legs, that is:

AB² = AC² + CB², and from this it follows that

AC² = AB² – CB² = 13² – 12² = 169 – 144 = 25

AC = √25 = 5cm

Answer: AC = 5 cm; CB = 12 cm.