Question

In a △ABC, if AB=2x - 1, AC=$2\sqrt{2x}$ and BC=2x + 1. Find the ∠BAC.

Answer 1

In △ABC:
${\left(AB\right)}^2={(2x-1)}^2=4x^2-4x+1{\left(AC\right)}^2={\left(2\sqrt{2x}\right)}^2=8x{\left(BC\right)}^2={(2x+1)}^2=4x^2+4x+1$

Now,
${\left(AB\right)}^2+{\left(AC\right)}^2=4x^2-4x+1+8x=4x^2+4x+1={\left(BC\right)}^2$

So △ABC is a right angled triangle and side AB and AC forms the right angle

So $\angle BAC=90°$