In the adjoining figure, ΔABC is right-angled at B and A= 45°. If AC = 3√2 cm, find (i) BC, (ii) AB.

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 45° = BC/AC


1/√2 = BC / (3√2)


BC = (1/√2) × (3√2) = 3


BC = 3 cm


(ii) Now, In the given figure, cos 45° = AB/AC


1/√2 = AB / (3√2)


AB = 1/√2 × (3√2)


AB = 3 cm


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