In a right triangle ABC, ∠B = 90°

(a) If AB = 6 cm, BC = 8 cm, find AC

(b) If AC = 13 cm, BC = 5 cm, find AB

(a) It is given that ΔABC is right-angled at B, hence the side opposite to angle B ie AC will be the hypotenuse. 


Therefore, by using Pythagoras theorem, we get:


AC2 = AB2 + BC2


AC2 = (6 cm)2 + (8 cm)2


AC2 = (36 + 64) cm2


AC2=100 cm2
or AC= cm


AC = 10 cm


 


(b) It is given that ΔABC is right-angled at B


Therefore, by using Pythagoras theorem, we get:


AC2 = AB2 + BC2


(13 cm)2 = (AB)2 + (5 cm)2


AB2 = (13 cm)2 - (5 cm)2


AB2 = 169 cm2 - 25cm2


AB2 = 144 cm2
or AB =  cm


AB = 12 cm

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