Since, in a right-angled triangle,

sin θ = Perpendicular / Hypotenuse,

and cos θ = Base / Hypotenuse,

where θ is the angle made between the hypotenuse and the base.

(i) In the given figure, sin 30° = BC/AC

1/2 = 6/AC

AC = 6 × 2

AC = 12 cm

(ii) Now, In the given figure, cos 30° = AB/AC

√3/2 = AB/12

(√3/2) × 12 = AB

AB = 6√3 cm

Aliter: Since ABC is a right-angled triangle,

(AB)2 +(BC)2 = (AC)2

(AB)2 = (AC)2 - (BC)2

(AB)2 = 144 – 36 = 108

(AB) = √108 = 6√3

AB = 6√3 cm

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