Knowing the cosine of the angle BAC, we determine the sine of this angle.
Cos2BAC + Sin2BAC = 1.
Sin2BAC = 1 – Cos2BAC = 1 – (√7 / 4) ^ 2 = 1 – 7/16 = 9/16.
SinBAC = 3/4.
Since BH is the height, then triangle ABH is rectangular, then through the leg BH and the sine of the opposite angle we determine the length of the hypotenuse AB.
AB = BH / SinBAC = 6 / (3/4) = 6 * 4/3 = 8 cm.
Answer: The length of the AB side is 8 cm.
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