In a right-angled triangle ABC, we define the sine of the angle BAC.
Cos2BAC + Sin2BAC = 1.
Sin2BAC = 1 – Cos2BAC = 1 – (3/5) 2 = 1 – 9/25 = 16/25.
SinBAC = 4/5.
Through the sine of the angle BAC and the length of the opposite leg, we determine the length of the hypotenuse AB.
SinBAC = BC / AB.
AB = BC / SinBAC = 12 / (4/5) = 12 * 5/4 = 15 cm.
Answer: The length of the hypotenuse AB is 15 cm.
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