The cosine of the angle of a right-angled triangle is the ratio of the adjacent leg to the angle to the hypotenuse of the triangle.
CosBAC = AB / AC = 3 * √3 / 6 = √3 / 2.
Angle BAC = arcos (√3 / 2).
Angle BAC = 60.
The sum of the angles of the triangle is 180, then the angle ACB = 180 – 90 – 60 = 30.
Answer: The acute angles of the triangle are 30 and 60.
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