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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:

AC^{2} = AB^{2} + BC^{2}

AC^{2} = (6 cm)^{2} + (8 cm)^{2}

AC^{2} = (36 + 64) cm^{2}

AC^{2}=100 cm^{2}or AC= cm

AC = 10 cm

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

Therefore, by using Pythagoras theorem, we get:

AC^{2} = AB^{2} + BC^{2}

(13 cm)^{2} = (AB)^{2} + (5 cm)^{2}

AB^{2} = (13 cm)^{2} - (5 cm)^{2}

AB^{2} = 169 cm^{2 }- 25cm^{2}

AB^{2} = 144 cm^{2}or AB = cm

AB = 12 cm

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