Question

In a $\Delta ABC$, if $A{C}^2=A{B}^2+B{C}^2$ then the right angle is at__

• A. C
• B. B
• C. A
• D. None of these

Answer 1

The correct option is B B

Pythagoras theorem,

$\Rightarrow$ $(Hypotenuse{)}^2=(Oneside{)}^2+(secondside{)}^2$ ---- ( 1 )

In $△ABC,$

$\Rightarrow$ $(AC{)}^2=(AB{)}^2+(BC{)}^2$ [ Given ] ----- ( 2 )

Comparing ( 1 ) and ( 2 ) we get,

$\Rightarrow$ $AC$ is the hypotenuse of a triangle.

Hypotenuse is the longest side of a right-angled triangle, opposite the right angle.

So, opposite angle of hypotenuse $AC$ is $B.$

$\therefore$ $B$ is right angle.

$\Rightarrow$ In $△ABC$ if $A{C}^2=A{B}^2+B{C}^2$ then the right angle is at $B.$