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.
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