Question

In a right angled triangle ABC. $\angle B={90}^o$.
(i) If AB = 6 cm , BC= 8 cm, find AC.
(ii) If AC = 13 cm, BC= 5 cm. find AB.

Answer 1

i) In $△ABC,\angle B={90}^o$

$\therefore$ By Pythagoras theorem,

$A{C}^2=A{B}^2+B{C}^2$

$A{C}^2=6^2+8^2$

$\therefore A{C}^2=36+64=100$

$\therefore AC=10$cm

ii) In $△ABC,\angle B={90}^o$

$\therefore$ By Pythagoras theorem,

$A{C}^2=A{B}^2+B{C}^2$

${13}^2=A{B}^2+5^2$

$\therefore A{B}^2=169-25=144$

$\therefore AB=12$cm