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Maths-

General

Easy

Question

If the sides of a triangle are in the ratio $x colon y colon square root of x squared plus x y plus y squared end root$ then greatest angle is

$90^{\circ}$
$120^{\circ}$
$\cos^{- 1} (\frac{x + y}{x - y})$
$60^{\circ}$

hint Hint:

In this question, we have to find the angle of the greatest angle. As c is the greatest side so angle C is the greatest angle. As we know the sides ratio, so using the cosine formula we will find the angle of the greatest side.

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

As the ratio of the sides is $x colon y colon square root of x squared plus x y plus y squared end root$
a= x, b=y, c = $square root of x squared plus x y plus y squared end root$
c is the largest side, so, C is the largest angle.
$cos space C space equals open parentheses fraction numerator a squared plus b squared minus c squared over denominator 2 a b end fraction close parentheses space space space space space space space space space space space equals open parentheses fraction numerator x squared plus y squared minus open parentheses x squared plus x y plus y squared close parentheses over denominator 2 x y end fraction close parentheses space space space space space space space space space space space equals open parentheses fraction numerator x squared plus y squared minus x squared minus y squared minus x y over denominator 2 x y end fraction close parentheses space space space space space space space space space space space equals fraction numerator negative x y over denominator 2 x y end fraction space space space space space space space space space space equals fraction numerator negative 1 over denominator 2 end fraction rightwards double arrow cos space C equals cos space 120 degree rightwards double arrow C equals 120 degree$
So, the angle of the greatest angle is 120 $degree$ .

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