Question

Traingle ABC is right angled at C. If AB is 20 cm and BC is 12 cm, find AC.

Answer 1

Given that,

$\Delta ABC$ is a right angled triangle, right angled at $C$.

$AB$ is $20cm$ and $BC$ is $12cm$

To find out,

The length of $AC$

If the $\Delta$ is right angled at $C$, then $AB$ will be the hypotenuse of the triangle.

Hence, by Pythagoras theoerm,

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

Hence, $AC=\sqrt{A{B}^2-B{C}^2}$

$\Rightarrow AC=\sqrt{{20}^2-{12}^2}$

$\Rightarrow AC=\sqrt{400-144}$

$\Rightarrow AC=\sqrt{256}$

$\Rightarrow AC=16cm$

Hence, the length of $AC$ is $16cm$.