Given a right-angled triangle ABC; hypotenuse AB = 8 angle BAC 60 ‘BС =? AC?

1) It is known that sin (60o) = √3 / 2, and cos (60o) = 1/2.
2) On the other hand, by the definition of cosine cos (60o) = AC / AB. By definition of sine sin (60o) = BC / AB.
3) From these ratios we get: AC = AB * cos (60o), BC = AB * sin (60o).
4) Substitute the sine and cosine values from the first point and AB = 8, we find AC and BC: AC = 8 * (1/2) = 4, BC = 8 * (√3 / 2) = 4√3.
ANSWER: AC = 4, BC = 4√3.