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In a $ΔABC$ , if $A C^{2} = A B^{2} + B C^{2}$ then the right angle is at which vertex?

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None of these

answer is B.

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Detailed Solution

Given equation

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

.
It is figure of a right angle triangle,
Question Image

By using pythagoras theorem,

\Rightarrow

(Hypotenuse)^{2} = (base)^{2} + (height)^{2}

---- ( 1 )
In

△ ABC,

\Rightarrow

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

[ Given ] ----- ( 2 )
Comparing ( 1 ) and ( 2 ) we get,

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

B .

∴

B

is right angle.
In

△ ABC

, if

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

then the right angle is at

B .

Hence, the correct option is 2.

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