In the adjoining figure, ΔABC ABC is right-angled at B and A= 30°. If BC = 6 cm, find (i) AB, (ii) AC.

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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