If the angles of a triangle are in the ratio 1 : 2 : 7, then the ratio of the greatest side to the least side, is

If the angles of a triangle are in the ratio 1 : 2 : 7, then the ratio of the greatest side to the least side, is

  1. A

    (51):(5+1)

  2. B

    (5+1):(51)

  3. C

    (5+2):(52)

  4. D

    (52):(5+2)

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    Solution:

    Let the angles of triangle ABC be A=θ, B = 2θ and C=7θ. Then,

    A+B+C=18010θ=180θ=18 A=18,B=36 and C=126

    Clearly, c is the greatest side and a is the smallest side. 

    Now,

    asinA=csinCca=sinCsinA=sin126sin18=cos36sin18=5+151

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