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

  1. 900
  2. 1200
  3. cos to the power of negative 1 end exponent space open parentheses fraction numerator x plus y over denominator x minus y end fraction close parentheses
  4. 600

hintHint:

The law of cosines generalizes the Pythagorean formula to all triangles. It says that c2, the square of one side of the triangle, is equal to a2 + b2, the sum of the squares of the the other two sides, minus 2ab cos C, twice their product times the cosine of the opposite angle. When the angle C is right, it becomes the Pythagorean formula.
law of cosines

The correct answer is: 1200


    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

    I n space increment A B C space comma l e t space s i d e space a comma space b space a n d space c space t h e n comma
a equals x comma space b equals y comma space c equals square root of x squared plus x y plus y squared end root
bold italic W bold italic e bold space bold italic k bold italic n bold italic o bold italic w bold space bold italic t bold italic h bold italic a bold italic t bold space bold italic t bold italic h bold italic e bold space bold italic a bold italic n bold italic g bold italic l bold italic e bold space bold italic o bold italic p bold italic p bold italic o bold italic s bold italic i bold italic t bold italic e bold space bold italic t bold italic o bold space bold italic t bold italic h bold italic e bold space bold italic l bold italic o bold italic n bold italic g bold italic e bold italic s bold italic t bold space bold italic s bold italic i bold italic d bold italic e bold space bold italic w bold italic i bold italic l bold italic l bold space bold italic h bold italic a bold italic v bold italic e bold space bold italic t bold italic h bold italic e bold space bold italic l bold italic a bold italic r bold italic g bold italic e bold italic s bold italic t bold space bold italic v bold italic a bold italic l bold italic u bold italic e bold. bold left parenthesis bold italic H bold italic e bold italic r bold italic e bold space bold italic c bold space bold italic s bold italic i bold italic d bold italic e bold space bold italic i bold italic s bold space bold italic g bold italic r bold italic e bold italic a bold italic t bold italic e bold italic r bold space bold italic t bold italic h bold italic a bold italic n bold space bold italic o bold italic t bold italic h bold italic e bold italic r bold italic s bold. bold right parenthesis
bold italic S bold italic o bold comma bold space bold cos bold space bold italic C bold space bold equals bold space fraction numerator bold a to the power of bold 2 bold plus bold b to the power of bold 2 bold minus bold c to the power of bold 2 over denominator bold 2 bold a bold b end fraction
cos space C space equals space fraction numerator x squared plus y squared minus x squared minus x y minus y squared over denominator 2 xy end fraction
cos space C space equals space fraction numerator negative x y over denominator 2 xy end fraction
cos space C space equals space fraction numerator negative 1 over denominator 2 end fraction
bold italic s bold italic o bold comma bold space bold italic A bold italic n bold italic g bold italic l bold italic e bold space bold italic C bold space bold equals bold space bold 120 bold degree
    Angle c is greatest in triangle.
    img

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