In the figure (2) given below, ∆ABC is right-angled at B. If AB = y units, BC = 3 units and CA = 5 units, find (i) sin x° (ii) y.

(i) By formula, sin x° = = . Hence, sin x° = . (ii) In right-angled ∆ABC Using pythagoras theorem ⇒ AC 2 = BC 2 + AB 2 ⇒ AB 2 = AC 2 - BC 2 ⇒ y 2 = 5 2 - 3 2 ⇒ y 2 = 25 - 9 ⇒ y 2 = 16 ⇒ y = ⇒ y = 4. Hence, y = 4 units.