Question
In $\triangle A B C$, if $a=2, b=3, c=4$ then prove that the triangle is obtuse angled.
✓
Answer
We know that the angle opposite to largest side of a triangle is the largest angle of the triangle.
Here side $AB$ is the largest side. $C$ is the largest angle of $\triangle ABC$. To show that $C$ is obtuse angle.
$
\cos C =\frac{a^2+b^2-c^2}{2 a b}=\frac{2^2+3^2-4^2}{2(3)(4)}=-\frac{3}{24}=-\frac{1}{8}
$
As $\cos C$ is negative, $C$ is obtuse angle.
$\therefore \quad \triangle ABC$ is obtuse angled triangle.
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