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.
Pythagoras Theorem : In a right angles triangle, square of the hypotenuse is equal to the sum of squares of other two sides.
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 Δ ABC is right-angled at B
Pythagoras Theorem : In a right angles triangle, square of the hypotenuse is equal to the sum of squares of other two sides.
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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