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

  1. 90 to the power of ring operator
  2. 120 to the power of ring operator
  3. c o s to the power of left parenthesis minus 1 right parenthesis invisible function application left parenthesis left parenthesis x plus y right parenthesis divided by left parenthesis x minus y right parenthesis right parenthesis
  4. 60 to the power of ring operator

hintHint:

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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