Maths-
General
Easy

Question

The sides of a triangle are sin space alpha comma cos space alpha and square root of 1 plus sin space alpha cos space alpha end root for some 0 less than alpha less than pi over 2.Then the greatest angle of the triangle is

  1. 600
  2. 1500
  3. 1200
  4. 900

hintHint:

 The angles of the triangle ABC are denoted by A, B, C and the corresponding opposite sides by a, b, c.

The correct answer is: 1200



    The sides of a triangle are sin space alpha comma cos space alpha and square root of 1 plus sin space alpha cos space alpha end root for some 0 less than alpha less than pi over 2.

    I n space increment A B C comma space
L e t space s i d e space a comma space b space a n d space c space t h e n space a equals sin alpha comma space b equals cos alpha comma space c equals square root of 1 plus sin alpha cos alpha 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 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
space cos space C space equals space fraction numerator sin squared alpha plus c o straight s squared straight alpha minus 1 minus sin alpha cos alpha over denominator 2 sin straight alpha cos straight alpha end fraction space space space space left curly bracket space 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 semicolon bold space bold italic s bold italic i bold italic n to the power of bold 2 bold space bold italic theta bold space bold plus bold space bold italic c bold italic o bold italic s to the power of bold 2 bold space bold italic theta bold space bold equals bold space bold 1 right curly bracket
cos space C space equals space fraction numerator negative sin alpha cos alpha over denominator 2 sin straight alpha cos straight alpha end fraction bold rightwards double arrow cos space C space equals space fraction numerator negative 1 over denominator 2 end fraction
cos space C space equals space fraction numerator negative 1 over denominator 2 end fraction space o r space A n g l e space C space equals 120 degree space
s o comma space G r e a t e s t space a n g l e space i s space C space I n space increment A B C. space space
    img

    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

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