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Maths-

General

Easy

Question

If the sides of a triangle are in the ratio $x colon y colon √ left parenthesis x squared plus x y plus y squared right parenthesis$ then greatest angle is

$90^{\circ}$
$120^{\circ}$
$c o s^{(} - 1) ((x + y) / (x - y))$
$60^{\circ}$

hint Hint:

In this question first we have to check which side is greatest then the angle opposite to greatest side will be greatest. We will use Cosine Rule to find the angle $cos open parentheses C close parentheses equals fraction numerator a squared plus b squared minus c squared over denominator 2 a b end fraction$ .

The correct answer is: $120 to the power of ring operator$

In this question we are given the ratio of sides of a triangle $x colon y colon square root of x squared plus x y plus y squared end root$
Let the sides of the triangle be $a space equals space k x comma space b space equals k y comma space c space equals space k square root of x squared plus x y plus y squared end root$ where K is a constant.
It can be easily seen that $c$ is the largest side. We know that the side opposite to greatest angle is always greatest. So, $C$ will be the greatest angle.
By using Cosine Rule
$cos open parentheses C close parentheses equals fraction numerator a squared plus b squared minus c squared over denominator 2 a b end fraction$
By substituting the value of a, b, c in the above expression we get,
$cos open parentheses C close parentheses equals fraction numerator k squared x squared plus k squared y squared minus k squared left parenthesis x squared plus x y plus y squared right parenthesis over denominator 2 k squared x y end fraction$
=> $cos open parentheses C close parentheses equals fraction numerator k squared left parenthesis x squared plus y squared minus x squared minus x y minus y squared right parenthesis over denominator 2 k squared x y end fraction$
=> $cos open parentheses C close parentheses equals fraction numerator negative x y over denominator 2 x y end fraction$
=> $cos open parentheses C close parentheses equals fraction numerator negative 1 over denominator 2 end fraction$
=> $C space equals space 120 degree$

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