Question

In the given figure, angle $ACB={90}^0=$ angle $ACD$. If $AB=10cm,BC=6cm\text{and}AD=17cm$, find:

(i) $AC$

Answer 1

Applying Pythagoras Theorem to find length of perpendicular



Since, $\Delta ABC$ is a right angled triangle with vertex C,
According to Pythagoras theorem,


$(Hypotenuse{)}^2$ = $(Perpendicular{)}^2$ + $(Base{)}^2$

$(AB{)}^2$ = $(AC{)}^2$ + $(BC{)}^2$

$(10{)}^2$ = $(AC{)}^2$ + $(6{)}^2$

$100=(AC{)}^2+36$

$AC=\sqrt{100-36}$

$AC=\sqrt{64}$

$\therefore AC=8cm$