Through the tangent of the angle BAC, we determine the sine of this angle.
Sin2BAC = 1 / (1 + (1 / tg2BAC)) = 1 / (1 + 64/225) = 225/289.
SinBAC = 15/17.
Let us determine the length of the hypotenuse AB.
SinBAC = BC / AB.
AB = BC / CosBAC = 15 / (15/17) = 17 cm.
Answer: The length of the hypotenuse AB is 17 cm.
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