Question

The length of the sides of a triangle are $x,y$ and $\sqrt{x^2+y^2+xy}$. The measure of the greatest angle is:

• A. ${120}^o$
• B. ${150}^o$
• C. ${135}^o$
• D. None of these

Answer 1

The correct option is A ${120}^o$

Let $a=x;b=y;c=\sqrt{x^2+y^2+xy}$

Here, $c$ is the greatest side of the triangle

Using cosine rule,

$\Rightarrow 2ab\cos C=a^2+b^2-c^2$

$\Rightarrow 2xy\cos C=x^2+y^2-(\sqrt{x^2+y^2+xy}{)}^2$

$\Rightarrow 2xy\cos C=x^2+y^2-x^2-y^2-xy$

$\Rightarrow 2xy\cos C=-xy$

$\Rightarrow 2\cos C=-1$

$\Rightarrow \cos C=\frac{-1}{2}$

$\Rightarrow C={120}^0$