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